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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Evaluation of Indirect Tensile Test (IDT) Procedures for Low-Temperature Performance of Hot Mix Asphalt. Washington, DC: The National Academies Press. doi: 10.17226/13775.
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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Evaluation of Indirect Tensile Test (IDT) Procedures for Low-Temperature Performance of Hot Mix Asphalt. Washington, DC: The National Academies Press. doi: 10.17226/13775.
×
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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Evaluation of Indirect Tensile Test (IDT) Procedures for Low-Temperature Performance of Hot Mix Asphalt. Washington, DC: The National Academies Press. doi: 10.17226/13775.
×
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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Evaluation of Indirect Tensile Test (IDT) Procedures for Low-Temperature Performance of Hot Mix Asphalt. Washington, DC: The National Academies Press. doi: 10.17226/13775.
×
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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Evaluation of Indirect Tensile Test (IDT) Procedures for Low-Temperature Performance of Hot Mix Asphalt. Washington, DC: The National Academies Press. doi: 10.17226/13775.
×
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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Evaluation of Indirect Tensile Test (IDT) Procedures for Low-Temperature Performance of Hot Mix Asphalt. Washington, DC: The National Academies Press. doi: 10.17226/13775.
×
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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Evaluation of Indirect Tensile Test (IDT) Procedures for Low-Temperature Performance of Hot Mix Asphalt. Washington, DC: The National Academies Press. doi: 10.17226/13775.
×
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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Evaluation of Indirect Tensile Test (IDT) Procedures for Low-Temperature Performance of Hot Mix Asphalt. Washington, DC: The National Academies Press. doi: 10.17226/13775.
×
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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Evaluation of Indirect Tensile Test (IDT) Procedures for Low-Temperature Performance of Hot Mix Asphalt. Washington, DC: The National Academies Press. doi: 10.17226/13775.
×
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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Evaluation of Indirect Tensile Test (IDT) Procedures for Low-Temperature Performance of Hot Mix Asphalt. Washington, DC: The National Academies Press. doi: 10.17226/13775.
×
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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Evaluation of Indirect Tensile Test (IDT) Procedures for Low-Temperature Performance of Hot Mix Asphalt. Washington, DC: The National Academies Press. doi: 10.17226/13775.
×
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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Evaluation of Indirect Tensile Test (IDT) Procedures for Low-Temperature Performance of Hot Mix Asphalt. Washington, DC: The National Academies Press. doi: 10.17226/13775.
×
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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Evaluation of Indirect Tensile Test (IDT) Procedures for Low-Temperature Performance of Hot Mix Asphalt. Washington, DC: The National Academies Press. doi: 10.17226/13775.
×
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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Evaluation of Indirect Tensile Test (IDT) Procedures for Low-Temperature Performance of Hot Mix Asphalt. Washington, DC: The National Academies Press. doi: 10.17226/13775.
×
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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Evaluation of Indirect Tensile Test (IDT) Procedures for Low-Temperature Performance of Hot Mix Asphalt. Washington, DC: The National Academies Press. doi: 10.17226/13775.
×
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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Evaluation of Indirect Tensile Test (IDT) Procedures for Low-Temperature Performance of Hot Mix Asphalt. Washington, DC: The National Academies Press. doi: 10.17226/13775.
×
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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Evaluation of Indirect Tensile Test (IDT) Procedures for Low-Temperature Performance of Hot Mix Asphalt. Washington, DC: The National Academies Press. doi: 10.17226/13775.
×
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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Evaluation of Indirect Tensile Test (IDT) Procedures for Low-Temperature Performance of Hot Mix Asphalt. Washington, DC: The National Academies Press. doi: 10.17226/13775.
×
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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Evaluation of Indirect Tensile Test (IDT) Procedures for Low-Temperature Performance of Hot Mix Asphalt. Washington, DC: The National Academies Press. doi: 10.17226/13775.
×
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Suggested Citation:"Chapter 2 - Findings." National Academies of Sciences, Engineering, and Medicine. 2004. Evaluation of Indirect Tensile Test (IDT) Procedures for Low-Temperature Performance of Hot Mix Asphalt. Washington, DC: The National Academies Press. doi: 10.17226/13775.
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5REVIEW OF AASHTO T322 The discussion below is a summary of the most significant findings presented in Appendix A of this report, which presents a detailed review of AASHTO T322, and recent related work done as part of NCHRP Projects 9-19 and 1-37A. Readers interested in details on these topics should refer to this Appen- dix. These findings and resulting recommended changes to AASHTO T322 to improve the effectiveness and efficiency of this procedure were forwarded to the task force responsible for recommending revisions to this test method to AASHTO. AASHTO T322 consists of 17 sections: 1. Scope 2. Referenced Documents 3. Terminology 4. Summary of Method 5. Significance and Use 6. Apparatus 7. Hazards 8. Standardization 9. Sampling 10. Specimen Preparation and Preliminary Determinations 11. Tensile Creep/Strength Testing (Thermal Cracking Analysis) 12. Tensile Strength Testing (Fatigue Cracking Analysis) 13. Calculations 14. Report 15. Precision and Bias 16. Keywords 17. References Many of these sections are only of nominal significance and have not been addressed as part of this study. Of special signif- icance are Sections 6. Apparatus, 10. Specimen Preparation, and 11. Tensile Creep/Strength Testing. The most signifi- cant findings of this study on these three critical sections of AASHTO T322 are summarized below. The specifications for the IDT creep and strength device, as currently given in AASHTO T322, are listed in Table 1. A careful review of these requirements has found several problems with the ranges and sensitivities for the various devices and transducers comprising the IDT test system (see Appendix A). The evaluations have been based upon typical properties of HMA at low temperatures, the fundamental stress-strain relationships for the IDT loading geometry, and typical cost-performance characteristics for loading systems, environmental chambers, and transducers. When appropriate, consistency with suggested requirements for the simple perfor- mance test has been considered in evaluating the requirements for the IDT system. As an example of the nature of the evaluation performed on the requirements summarized in Table 1, consider the speci- fications for the range for the axial loading device. In SHRP Report A-357, the developer of the IDT creep and strength testing procedure presents data for a range of mixtures (1). These exhibit a range in compliance values of from about 3 × 10−11 Pa−1 to 4 × 10−9 Pa−1. Because the linear range for HMA occurs at strains less than or equal to 0.05 percent, the maximum applied tensile stresses corresponding to these compliance values range from 125 kPa to 17 MPa. Based upon the relationship σt = 2P/πtD, the axial loads corre- sponding to these tensile stresses are 1.5 and 200 kN, respec- tively, for a specimen 50 mm thick and 150 mm in diame- ter. However, another consideration is the maximum load that can be applied without a specimen failing. The lowest tensile strength (σt) reported in SHRP A-357 was 1.3 MPa, and the highest was 4.3 MPa. The corresponding load (P) for these tensile strengths can be calculated as P = σtπtD/2, where t and D are the specimen thickness and diameter, respectively. The calculated loads based on tensile failure are between 15 and 51 kN for a specimen 50 mm thick. Limiting the load to one-half that required to cause failure and allowing for specimens up to 100 mm in thickness, the antic- ipated maximum load is then 50 kN. However, to ensure good loading system performance, the capacity of the loading system should be about double the anticipated maximum load, giving a maximum capacity of 100 kN, agreeing nearly exactly with the 98 kN given in AASHTO T322. Evaluation of the displacement rate is more detailed and is presented in Appendix A. In the previous example, the requirements in AASHTO T322 for the range of the axial loading device appear to be reasonable. However, the sensitivity requirements appear to be too stringent. Consider the worst-case situation, which is for the lowest anticipated load. Because it would be undesir- able to approach nonlinearity, in some cases the applied loads might be somewhat less than the estimated minimum load of 1.5 kN, say 1 kN. To calibrate to this load level, ASTM E4 requires a resolution that is 1/100th of the minimum load level or a resolution of 10 N, which is significantly larger (poorer) than the 5-N resolution requirement given in AASHTO T322. Consideration should be given to changing CHAPTER 2 FINDINGS

the required resolution for the IDT loading system to 10 kN; this would likely reduce the cost of the equipment required to perform the test. Various aspects of the equipment specifications, as pre- sented previously in Table 1, were evaluated in detail. The recommended revised specifications for the IDT creep and strength test are given in Table 2. In many cases, the changes are slight, such as rounding the maximum load to 100 kN rather than 98 kN, or the recom- mended 0.1 µm sensitivity for the deformation measuring devices compared with the original 0.125 µm sensitivity. The most substantial changes are probably the less stringent requirements for the sensitivity of the axial loading device and load cell (increased to 10 N from 5 N) and the change in the required range of the environmental chamber from −30 to +30°C to −30 to +10°C. Both of these changes should help reduce the cost of the IDT system. Requirements for specimen preparation in AASHTO T322 are currently vague and should be stated more explicitly to ensure good test data. Table 3 and the accompanying notes list suggested requirements for IDT creep and strength spec- imens. The values given in this table have largely been based on requirements for specimen uniformity developed during NCHRP Project 9-29 for the simple performance tests (6). Maintaining similar requirements for both tests will ensure that technicians are familiar with these standards and that the equipment and techniques needed to produce such specimens are available in most laboratories. Currently the suggested test temperatures for the creep pro- cedure are 0, −10, and −20°C. Because of the variability in binder grades and the resulting low-temperature properties of asphalt concrete, some specimens are extremely stiff at −20°C, while others may be too compliant at 0°C. The test temperatures used in the IDT creep and strength tests should, 6 Component General Requirements Range Sensitivity Axial loading device Shall provide a constant load 98 kN maximum load; Displacement rate between 12 and 75 mm/min 5 N minimum Load measuring device Electronic load cell 98 kN minimum capacity 5 N minimum Deformation measuring device(s) Four linear variable differential transducers (LVDTs) 0.25 mm minimum 0.125 µm minimum Environmental chamber Temperature control only; large enough to perform test and condition 3 specimens -30 to +30 °C Control to ±0.2 °C Control and data acquisition system Shall digitally record load and deformation during test 1 to 20 Hz sampling rate 16-bit A/D board required Test fixture As described in ASTM D4123 (diametral resilient modulus testing) N/A 2 kg maximum frictional resistance TABLE 1 AASHTO T322 specifications for IDT apparatus Component General Requirements Range Sensitivity Axial loading device Shall provide a constant load 100 kN maximum load; Maximum displacement rate of at least 12 mm/min 10 N or better Load measuring device Electronic load cell 100 kN minimum capacity 10 N or better Deformation measuring device(s) Four displacement transducers (LVDTs) 0.1 mm minimum 0.1 µm or better Environmental chamber Temperature control only; large enough to perform test and condition 3 specimens -30 to +10 °C under ambient conditions of 15 to 27 °C Control to ±0.5 °C Control and data acquisition system System shall be operated with the use of a personal computer and shall digitally record load and deformation during test 1 to 20 Hz sampling rate Consistent with required sensitivity of all system transducers Test fixture As described in ASTM D4123 (diametral resilient modulus testing), but with flat neoprene loading strips 12-mm thick by 12-mm wide. N/A 20 N maximum frictional resistance TABLE 2 Proposed revised AASHTO T322 specifications for the IDT apparatus

7therefore, change according to the binder grade used. The relationship between binder stiffness and mixture stiffness is not 1:1; a given change in binder stiffness will produce a somewhat lower change in mixture stiffness. It is suggested that the current test temperatures of 0, −10, and −20°C be maintained for mixtures made using PG XX-22 and PG XX-28 binders. For PG XX-16 and PG XX-10 binders or mixtures that have been severely age-hardened, the recom- mended test temperatures should be −10, 0, and +10°C. For PG XX-34 binders (or softer), the recommended test temper- atures should be −30, −20, and −10°C. A related problem with the current version of AASHTO T322 is that the test conditions must be determined through a trial-and-error procedure. A load is applied to the speci- men; if the resulting strains fall outside the allowable range, the test is aborted, the specimen is allowed to recover for 5 minutes, and the test is then repeated at an adjusted load level. No suggestions are given concerning what the appro- priate applied loads should be for different combinations of mixture types and test conditions. Given the suggested revised protocol above, it is possible to provide guidelines for the applied load, as listed in Table 4. The specimen would initially be tested using the initial applied load listed in the second column of Table 4. If the resulting deformations are too small or too large, the test should be aborted, the specimen allowed to recover, and the test repeated using the alternative loads listed in the third column of Table 4. In general, most of the recommended modifications to AASHTO T322 are minor and not controversial; therefore, they should be easy to implement. The suggested revisions contained in this report have been forwarded to the task force responsible for recommending revisions to this test method to AASHTO. EXPERIENCE WITH THE IDT TEST AT THE REGIONAL SUPERPAVE CENTERS In the late 1990s, IDT test systems were procured by the FHWA for four of the five Regional Superpave Centers. These test systems were to be used for further evaluation of the IDT creep and strength test procedures. The systems were unusual in that they were closed-loop electro-mechanical sys- tems, rather than the much more traditional closed-loop servo- hydraulic systems usually used for IDT tests and other similar procedures. Unfortunately, these test systems were plagued with more or less constant hardware and software problems. These problems were not the results of any inherent flaws in the basic concepts underlying the IDT creep and strength tests, but were the result of typical problems in first-article prototypes, exacerbated by a lack of technical support by the vendor and limited support funds available for performing needed modifications to the IDT systems. This experience has, however, made it unlikely that similar electro-mechanical sys- tems can be effectively implemented for use in IDT testing in the near future. One aspect of the experience among the Superpave Cen- ters that should be given consideration is their abandonment of using Linear Variable Differential Transformers (LVDTs) during the IDT strength test to determine the exact moment of failure. In a standard IDT strength test, the precise moment of failure, and hence the “true” tensile strength, is difficult to determine, because the specimen fails very grad- ually and continues to carry substantial load even after large cracks appear. During SHRP, the suggested solution to this problem was to use the horizontal and vertical LVDTs to Item Specification Remarks Average diameter 150 to 154 mm See Note 1 Standard deviation of diameter 1.0 mm See Note 1 Average thickness 40 to 60 mm See Note 2 Standard deviation of thickness 1.0 mm See Note 2 Smoothness 0.3 mm See Note 3 Table 3 Notes: 1. Measure the diameter at the center and third points of the test specimen along axes that are 90 degrees apart. Record each of the six measurements to the nearest 1 mm. Calculate the average and the standard deviation of the six measurements. The standard deviation shall be less than 1.0 mm. The average diameter, reported to the nearest 1 mm, shall be used in all material property calculations. 2. Measure the thickness of the specimen to the nearest 1 mm at eight equally spaced points along the circumference of the specimen, using a pair of calipers or other similar device. Calculate and report the average thickness to the nearest 1 mm. The standard deviation of the specimen thickness shall be less than 1.0 mm. The average thickness shall be used in all material property calculations. 3. Check this requirement using a straight edge and feeler gauges. TABLE 3 IDT creep and strength specimen requirements Test Temperature Initial Applied Load (kN) Other Possible Applied Loads (kN) Lowest 40 Deformation < 0.01 mm: 80 Deformation > 0.02 mm: 20, 10 Intermediate 10 Deformation < 0.01 mm: 20, 40 Deformation > 0.02 mm: 5, 2 Highest 5 Deformation < 0.01 mm: 10, 20 Deformation > 0.02 mm: 2, 1 TABLE 4 Guidelines for applied load in the IDT creep test

monitor horizontal and vertical deflections during the strength test. The point of failure is defined as occurring when the difference between the vertical and horizontal deformations reaches a maximum. Unfortunately, keeping LVDTs in place during the strength test often results in dam- age or destruction to these sensitive and expensive transduc- ers. Engineers within the Superpave Centers agreed that, for practical reasons, the IDT strength test should be done without LVDTs, and the strength based only upon the maximum load. Although the SHRP procedure is more accurate, it appears that it is impractical, and damage to the LVDTs because of this procedure could actually reduce the overall reliability of the IDT creep and strength tests. The relationship between cor- rected and uncorrected IDT strength were evaluated experi- mentally in this project, and a relatively accurate empirical equation for estimating the true IDT strength from the un- corrected strength (based on maximum load) was developed. These results, along with other data and analyses constituting the laboratory testing portion of Phase III of NCHRP Project 9-29, are presented later in this chapter. REFINEMENTS IN THE IDT TEST DURING NCHRP PROJECTS 1-37A AND 9-19 One of the early work elements in the Superpave Support and Performance Models Management Project (FHWA Con- tract DTFH61-95-C-00100, later NCHRP Project 9-19) was an evaluation of the Superpave low-temperature cracking model. A report on this work element was compiled, which documented numerous problems in the original SHRP ther- mal cracking model (7 ). A large number of minor problems in the program and its interface with the main SHRP mixture program were documented, along with a number of poten- tially more serious conceptual problems. One such issue was the use of an equation to estimate the coefficient of thermal contraction, α, of asphalt concrete mixtures, rather than an actual measurement. Research has suggested that the recom- mended equation for estimating α is not accurate (8), but available experimental procedures for measuring α have not been widely used and have not been thoroughly evaluated (9). A simple, improved equation for estimating the coefficient of thermal contraction for mixtures has been developed as part of this project and is presented later in this chapter in a sec- tion devoted to theoretical considerations of IDT creep and strength testing. Two other potentially serious problems noted by Janoo and his coauthors (7) were the use of a very short, 100-second creep loading time and the characterization of mixture ten- sile strength using a single measurement at −10°C rather than with a number of measurements over a range of tempera- tures. However, improvements in the algorithm for generat- ing compliance master curves have made the use of short creep tests more reliable (5). Use of only one tensile strength value in the computer program should also be acceptable, because tensile strength is simply one of several inputs used to estimate fracture properties and predict thermal cracking using the calibrated Superpave thermal cracking model. 8 In summary, the current version of the IDT test and analy- sis procedure has been substantially improved to address many of the shortcomings found immediately after the con- clusion of SHRP. The following changes have been incorpo- rated into the most recent version of the IDT test procedure and Superpave thermal cracking software: • Simplified formulas have been developed for making correction factors for specimen bulging and non-uniform stress and strain distribution across the specimen; • The initial portion of data analysis, which involves devel- oping a “trimmed” mean for the response of a given set of specimens, has been enhanced to avoid problems that occurred when a transducer was not responding and also to provide the user an overall indication of the quality of the data being analyzed; • The procedure used to shift the individual compliance curves to form a master compliance curve has been sub- stantially improved and is more robust and produces reasonable and repeatable master curves even for non- ideal data; • Most or all of the minor problems (“bugs”) in the original Superpave computer program have been corrected; and • The entire program has been recalibrated with an ex- panded data set, which includes the original mixtures and pavements used during SHRP and additional ma- terials and pavements from the Canadian SHRP program. Potential problems that have not been addressed include a potentially inaccurate estimate of the coefficient of ther- mal contraction and use of LVDTs during the IDT strength test, which often damages the LVDTs and can result in the collection of faulty data for subsequent creep and strength tests. PRECISION AND BIAS OF THE IDT TESTER One of the main objectives of this study was to make a pre- liminary estimate of the precision of the IDT creep and strength test procedures. Although it had been planned to perform ruggedness testing using the IDT test systems at the Superpave Centers, the many problems with these systems prevented the completion of a thorough ruggedness test program. However, ruggedness testing was performed on the IDT strength test under Contract DTFH61-95-C-00055, as reported by Anderson and McGennis (3). The results of this testing are summarized below. As part of Phase III of NCHRP Project 9-29, creep data were collected from six laboratories around the country and summarized and analyzed statistically, as described below, in order to provide estimates of the precision of this procedure. Precision of the IDT Strength Test Three laboratories participated in the IDT strength rugged- ness study: FHWA’s TFHRC, the Northeast Superpave Cen- ter (NESC), and the Asphalt Institute (TAI) (3). The objec-

9tive of ruggedness testing is to evaluate the effect of slight variations in important aspects of test conditions on the test results. An estimate of the precision of the test method is also generally possible. Factors evaluated in the IDT strength ruggedness testing included air voids, preload, temperature, temperature preconditioning, temperature stabilization time, loading rate, and specimen orientation. These tests were con- ducted at a nominal temperature of −10°C, which is the stan- dard temperature for performing the IDT strength test (3). Anderson and McGennis found that none of the main fac- tors evaluated had a statistically significant effect on the IDT strength test (3). However, it should be kept in mind that improvements in the precision of this procedure could result in different conclusions in the future. It was recommended that current tolerances on test temperature (±0.2°C) and requirements for preconditioning time (3 ± 1 hour) be main- tained. It was also suggested that specimens be stabilized for 45 minutes prior to testing, unless a given laboratory can document that shorter conditioning times are effective, though specimens should in any case be conditioned for at least 15 minutes prior to testing. Current requirements for loading rate and initial preload appeared to be adequate, as did the tolerance for air void content (3). Anderson and McGennis suggested that further studies be conducted to evaluate an air void tolerance of 7.0 ± 1.0 percent, in order to simplify spec- imen preparation (3). The overall average value of tensile strength for the rugged- ness study was 2870 kPa (415 lb/in2). The pooled standard deviation was 346 kPa (50.1 lb/in2), which is for a single repli- cate determination (3). Normally, three independent deter- minations are averaged in an IDT strength test, so statistics should be calculated for n = 3. In this case, the standard error would be 200 kPa (29.0 lb/in2), and the coefficient of variation 7.0 percent. A common and convenient statistic for character- izing the precision of a test method is the d2s precision. The term “d2s” stands for “difference, 2 standard deviations,” and represents the maximum expected difference between two independent measurements, in this case for a single oper- ator within one laboratory. The d2s precision is calculated as × SE, where SE is the standard error based upon an aver- age of several measurements—in this case three measure- ments. The d2s can be expressed in absolute terms—in units of kPa in this case—or as a percentage of the mean response. For the strength data reported by Anderson and McGennis, the d2s precision is 19.7 percent, expressed as a percentage of the mean (3). Considering the generally high variability observed in strength test data, this level of precision is prob- ably acceptable. Precision Evaluation of the IDT Creep Test As part of Phase III of NCHRP Project 9-29, numerous laboratories that have IDT creep and strength test systems were contacted and asked to provide data for the purposes of evaluating the precision of IDT creep data. These laborato- ries were told the results of the study would be anonymous, 2 2 so detailed information concerning the various laboratories cannot be provided. The nature of the six organizations is summarized briefly in Table 5. Data were requested for 5 or 6 different mixtures; each laboratory submitted data for 2 to 12 mixtures. No more than 6 mixtures were analyzed from each lab. Most of the labora- tories performed tests at −20, −10, and 0°C. Laboratory L3, however, performed tests at temperatures 10 to 20 degrees lower than this, perhaps because the binder grades repre- sented by their mixtures were softer than those normally used, although the resulting compliance data were significantly lower than typical. Most of the laboratories performed three replicate tests at each temperature, except Laboratory L4, which performed four replicates. Extensive information con- cerning the nature of the mixtures was not provided by the laboratories, though typical data were requested and for the most part were submitted. Table 6 is a summary of the data submitted by the six laboratories. The compliance data sub- mitted by the various laboratories were in a similar range, with the exception of Lab L3, which as mentioned previ- ously, performed their tests at significantly lower tempera- tures than normal. The replicates referred to in Table 6 were individual tests on the same mixture, which are normally averaged when reporting the final results of the IDT creep compliance test. In other words, this data set does not include full “true” repli- cation, in which the same mixture was tested repeatedly, in each case using three replicate measurements. However, the three individual measurements comprising a normal IDT creep test contain perfectly useful statistical information and can be treated as replicates for the purposes of evaluating the precision of the IDT creep test. In this study, the three (or in Laboratory Code Type of Organization Type of Test System L1 University Servo-hydraulic L2 Commercial Engineering, Research, and Testing Servo-hydraulic L3 Commercial Engineering, Research, and Testing Servo-hydraulic L4 Material Supplier Servo-hydraulic L5 Material Supplier Servo-hydraulic L6 Superpave Center Electro-mechanical TABLE 5 Description of laboratories participating in the precision study Lab. Code No. of Reps. Total No. of Tests Minimum Compliance (1/GPa) Maximum Compliance (1/GPa) L1 3 33 0.031 0.583 L2 3 36 0.030 0.511 L3 3 54 0.027 0.188 L4 4 96 0.032 0.543 L5 3 18 0.053 0.875 L6 3 36 0.046 0.737 All labs No. of Mixes 4 4 6 6 2 4 26 No. of Temp. 3 3 3 3 3 3 3 3-4 273 0.027 0.875 TABLE 6 Summary of data submitted for compliance precision study

one case four) individual measurements on each mix were analyzed separately to provide independent replicate deter- minations. These were then used to estimate an average value and a standard deviation for each mixture for a given laboratory. These values were then averaged over all mix- tures for a given laboratory. For standard deviation, the average was calculated as the square root of the average variance, which is the correct way of calculating an average or pooled standard deviation. Statistics were calculated for compliance, m-value (log-log slope of creep compliance), and Poisson’s ratio (ν). Because a normal IDT creep test consists of an average of three measurements, the standard deviation and coefficient of variation calculated as described above (for a single mea- surement) overestimate the variability in the standard pro- cedure. In order to estimate the standard deviation for the complete procedure (including full replication), the standard deviation for an average containing three replicates must be calculated—this is simply the standard deviation divided by the square root of 3. This is referred to in this report as the standard error (SE). Finally, the d2s precision was calcu- lated for each laboratory and temperature. Figures 1 through 4 graphically represent d2s precision esti- mates for compliance, m-value, Poisson’s ratio, and critical temperature (respectively) for the six laboratories involved in this study. For compliance (Figure 1) d2s precision is given as a percentage, while for m-value (Figure 2), Poisson’s ratio (Figure 3), and critical temperature (Figure 4), it is in absolute terms. Critical temperature is the temperature at which the cal- culated thermal stress equals the tensile strength; it represents the expected cracking temperature during a single extreme low-temperature event (10). This value was estimated using typical values for tensile strength (3.0 MPa) and coefficient of thermal expansion (1.1 × 10−5 m/m/°C), so that the variability was from compliance measurements only. The variability in compliance, in general, appears to in- crease with temperature and is generally in the range of about 10 to 30 percent, though it is somewhat higher for Lab L5 and Lab L6. Because data for only two mixtures were submitted for Lab L5, the variability estimates are not completely reli- able. The higher variability for Lab L6 is probably due to the 10 0 10 20 30 40 50 60 70 L1 L2 L3 L4 L5 L6 Avg. Laboratory d2 s Pr ec is io n fo r D( t), % Low Temp. Mid. Temp. High Temp. Figure 1. D2S precision for compliance for six laboratories. 0.00 0.02 0.04 0.06 0.08 0.10 Laboratory d2 s Pr ec is io n fo r m (t) Low Temp. Mid. Temp. High Temp. L1 L2 L3 L4 L5 L6 Avg. Figure 2. D2S precision for m(t) for six laboratories. 0.00 0.05 0.10 0.15 0.20 0.25 Laboratory d2 s Pr ec is io n fo r m u Low Temp. Mid. Temp. High Temp. L1 L2 L3 L4 L5 L6 Avg. Figure 3. D2S precision for Poisson’s ratio for six laboratories. 0 2 4 6 8 10 12 Avg. w/o Labs 3 and 6a Laboratory d2 s Pr ec is io n fo r T c, C a The reasons for excluding the results from Labs 3 and 6 from the average are given in the text. L1 L2 L3 L4 L5 L6 Avg. Figure 4. D2S precision for critical temperature for six laboratories. electro-mechanical test system used there, which, as dis- cussed previously, was one of the prototypes procured for the Superpave Centers that exhibited many software and hard- ware problems. The average d2s precision for all laboratories was 22, 28, and 32 percent at the lowest temperature, the middle temperature, and the highest temperature, respec- tively. Excluding data from Lab L6 would probably reduce these values to about 20 to 30 percent, which is somewhat high for single-operator precision values. If it is assumed that

11 interlaboratory d2s values are roughly twice single-operator values, the interlaboratory precision for compliance would be 40 to 60 percent, which is clearly too high. However, improvements in test equipment and procedures can proba- bly substantially improve the precision of this test. Similar trends are observed in d2s precision for m-value and Poisson’s ratio. The variability for Poisson’s ratio seems to be particularly high, given that the average values for ν were from 0.35 to 0.40. The poor precision for the determination of Pois- son’s ratio and the fact that this property is in general not con- sidered critical in determining resistance to low-temperature cracking, indicate that measurement of ν is not necessary for low-temperature characterization of asphalt concrete. It is of course a necessary part of the IDT procedure. The d2s precision values for critical temperature (Figure 4) range from slightly less than 2°C for Lab L2 to almost 12°C for Lab L3. However, the compliance data for Lab L3 was determined at very low temperatures, which is probably the reason for the extreme variability in critical temperatures. This emphasizes the importance of performing compliance mea- surements at appropriate temperatures. As discussed previ- ously, the compliance measurements for Lab L6 were done using an electro-mechanical test system and should also not be considered representative of the data quality possible with a good servo-hydraulic system. Eliminating these two labo- ratories, the average d2s precision for critical temperature was 2.9°C, equivalent to half a binder grade. Again, this is probably somewhat high considering that this is a single- operator value, but it should be possible to improve this value by further standardization of the low-temperature test equip- ment and procedure. Summary of Findings on Precision and Bias A summary of the various estimated statistics on the IDT creep and strength tests is presented in Table 7. These sta- tistics are based upon a test consisting of the average of three replicates. Because the statistics were calculated based upon replicate measurements conducted within each labo- ratory, the results correspond approximately to single-operator conditions; between-laboratory variability would be larger. The statistics on strength are based upon the data reported by Anderson and McGennis, as discussed previously (3). The statistics for IDT creep data are based upon data sub- mitted by six different laboratories, as described previously. The precision estimates for critical temperature were cal- culated without the data from Labs L3 and L6, because of the anomalously high variability in this statistic for these laboratories. The precision for the IDT strength test appears to be accept- able. The precision for the IDT compliance procedure, on the other hand, needs to be improved as part of the implementa- tion process. Ruggedness testing for this procedure is the next logical step in the development of this procedure. This testing should identify items in the procedure and equipment that sub- stantially affect the test precision. THEORY OF IDT TESTING AND ANALYSIS There are a number of theoretical considerations in the evaluation of both the IDT and uniaxial creep and strength tests. These include the following issues: • Linearity, • Homogeneity, • Anisotropy, • Poisson’s ratio, • Coefficient of thermal contraction, and • Estimation of relaxation modulus from creep compliance. These issues impact the test methods and analysis in a vari- ety of ways. They are discussed in detail in the following sections. Property Statistics Lowest Temp. Middle Temp. Highest Temp. Average, kPa 2870 Std. Error, kPa 200 C. V., % 7.0 Strength d2s, % N/A 19.7 N/A Average, 1/GPa 0.0463 0.0986 0.2809 Std. Error, 1/GPa 0.0042 0.0115 0.0413 C. V., % 7.9 9.9 11.3 Compliance d2s, % 22.3 28.0 32.0 Average 0.143 0.238 0.355 Std. Error 0.021 0.018 0.018 td Dd tm log log)( = d2s 0.061 0.051 0.052 Average 0.350 0.376 0.376 Std. Error 0.049 0.042 0.042 Poisson’s Ratio d2s 0.139 0.118 0.118 Average, °C -26.3 Std. Error, °C 1.0 Critical Temp. d2s, °C 2.9 TABLE 7 Summary of statistics on IDT creep and strength tests (n3 replicates)

Linearity The issue of linearity is of great practical importance. Intu- itively, asphalt concrete at low temperatures is expected to behave in a linear manner through loading approaching the point of failure, because of the high stiffness of asphalt con- crete under these conditions and the very low strains. It is, however, important to verify that the loads used in the IDT test are appropriate—as high as possible, to ensure large deflections and good repeatability, while still remaining in the linear viscoelastic region. AASHTO T322 calls for a maximum strain of 500 × 10−6 mm/mm, or 0.05 percent. This value is consistent with work performed by Mehta and Chris- tensen (11), who reported that deviations from linearity began to occur at the same strain level of 0.05 percent. This aspect of AASHTO T322 probably does not need revision. Homogeneity Homogeneity is the degree to which the properties of a material are the same at any given point. Most mechanical analyses, including those used to estimate mechanical prop- erties from both the IDT and uniaxial creep and strength tests, assume that a material is homogenous—that is, the properties are the same at any given location within the object consid- ered. However, asphalt concrete is clearly not truly homoge- nous, because it is composed of three distinct phases—asphalt binder, aggregate, and air. The question is, therefore, whether significant errors are involved in the assumption of homo- geneity in the analysis of IDT and uniaxial tests and in the analysis of thermal cracking in general. In general, the larger a specimen is compared to any nonuniformity it contains, the more accurate the assumption of homogeneity. For this rea- son, homogeneity is probably a very good assumption when analyzing an entire, intact paving system. However, for test specimens of relatively small size, homogeneity might not be even approximately obtained. Weissman and associates presented a detailed analysis of the effects of specimen dimension on the results of permanent deformation tests (12). They discussed the concept of the rep- resentative volume element (RVE), which in simple terms can be thought of as the minimum acceptable specimen dimension for a given test and material in order to ensure that the assump- tion of homogeneity is met. Meeting RVE requirements is an important contribution to test precision. Weissman and his coauthors suggested an RVE of 125 mm for an asphalt concrete mixture containing 19-mm nominal maximum size aggregate. In order to ensure that end effects were insignificant, this would mean that a uniaxial creep test would require a speci- men about 350 mm high by 125 mm in diameter (12). How- ever, this analysis dealt with permanent deformation tests, where the modulus of the aggregate is much greater than that of the surrounding mastic, a situation that greatly increases RVE size. For low-temperature tests, the RVE should be sig- nificantly smaller. Furthermore, because of the strip loading used in the IDT test and the correction factors developed for 12 this test during SHRP that should account for the triaxial loading conditions, end effects should not be a concern for this test. On the other hand, the typical 50-mm specimen thickness for the IDT is very small, as is the LVDT gage length of 37.5 mm. Without a detailed finite element analy- sis (which was beyond the scope of this study), it cannot be concluded with certainty whether RVE requirements have been met for either the IDT or uniaxial creep and strength tests at low temperature. One indication of whether the specimen size for the IDT and uniaxial tests is adequate is the precision of these meth- ods compared to what is possible for similar tests where spec- imen homogeneity is not an issue. For the IDT precision study described previously, the single-test coefficient of variation (C.V.) ranged from 14 to 20 percent. In the experiment phase of this project, presented later in this chapter, the single test C.V. for the IDT creep test was found to be 16 percent, which is in excellent agreement with the results of the interlabora- tory precision study. Mehta and Christensen reported C.V. values of 9 to 17 percent for relaxation tests performed using the IDT geometry (11). Pellinen reported in detail on the pre- cision of uniaxial dynamic modulus measurements using cylinders 100 mm in diameter by 150 mm high; her analysis broke the variability of the data into within- and between- specimen components (13). She reported overall C.V. values for a standard specimen with two LVDTs to be 15 to 21 per- cent for 12.5-mm mixtures and 17 to 24 percent for 19-mm mixtures (13). As a comparison, Christensen and Anderson reported C.V. values for complex modulus of asphalt binders—a very homogenous material compared to asphalt concrete—measured using a dynamic shear rheometer to range from 10 to 17 percent (14). Because of the complexity of preparing asphalt concrete specimens for testing, a some- what higher level of variability should be expected compared to data on asphalt binders. Therefore, it would appear that typ- ical precision levels for both the IDT and uniaxial modulus tests are consistent with a reasonable degree of homogeneity. Further improvements in test precision would provide addi- tional confidence that specimen homogeneity is not an issue with these procedures. Anisotropy Isotropic behavior is generally assumed when analyzing test data or performing stress and strain analyses. That is, it is assumed that the mechanical properties of the material in question are independent of direction and sense. Because of the manner in which asphalt concrete specimens and pave- ments are compacted, it is quite possible that asphalt con- crete is anisotropic, that its properties vary depending upon the direction of loading. Support for anisotropic behavior is seen in the relationships between uniaxial and shear moduli values reported by several researchers (4, 15). For an isotropic, linear elastic material, the uniaxial modulus E should be 2(1 + ν) G , where ν is Poisson’s ratio, typically ranging from about 0.3 to 0.5 for asphalt concrete and  G is the

13 shear modulus. Although the behavior of asphalt concrete under the conditions in question is linear viscoelastic rather than linear elastic, this relationship should apply quite well. However,  E values are normally much higher compared to  G than predicted by this relationship, indicating that there is substantial anisotropy in the behavior of asphalt con- crete mixtures (4). It appears that because of preferential orientation of aggregate particles during the shearing that occurs with compaction, the shear stiffness of mixtures per- pendicular to the plane of compaction is relatively low com- pared to the uniaxial compressive stiffness in the direction of compaction. The results of the laboratory testing performed as part of this project (described later in this chapter) indicate that the low-temperature creep compliance of asphalt concrete mix- tures does in fact exhibit anisotropy. The creep compliance measured in the diametral plane using the IDT test is less than that measured along the length of the specimen (uniaxially) in compression, which in turn is less than the compliance mea- sured in uniaxial tension. The effect of this anisotropy on the results of IDT and uniaxial stiffness tests is, however, not clear. On one hand, the IDT test has an advantage compared to the uniaxial test because the IDT procedure primarily mea- sures creep compliance in the horizontal plane, which is most important in thermal cracking. On the other hand, the analy- sis of the IDT test is based upon an assumption of isotropic behavior, and so the analysis is probably not completely accu- rate, because it appears that the properties in tension and compression are not identical. However, because the tensile strains in the IDT test are quite low, the difference in the tension and compression compliance values is probably small, resulting in a small effect on the IDT data analysis. In view of the apparent anisotropy in asphalt concrete mix- tures, the IDT test geometry is probably the most effective of the available methods for determining low-temperature creep compliance. Poisson’s Ratio Another issue in the IDT test procedure is whether it is truly necessary to determine Poisson’s ratio when characterizing the mechanical behavior of HMA at low temperature. Poisson’s ratio represents the ratio of lateral to axial deformation under uniaxial loading. It is theoretically necessary to know Pois- son’s ratio when performing stress analyses in two or three dimensions. However, in performing simple, one-dimensional stress analyses, such as those used in the Superpave thermal cracking analysis, Poisson’s ratio is not used. Furthermore, for most materials, Poisson’s ratio falls between about 0.2 and 0.5. For asphalt concrete, Huang states that values typi- cally fall in a narrower range, from 0.3 to 0.4 (16). Huang goes on to state, “Because Poisson’s ratio has a relatively small effect on pavement responses, it is customary to assume a reasonable value for use in design, rather than to determine it from actual tests” (16). It appears as though determination of Poisson’s ratio is not critical to the predic- tion of low-temperature cracking, again suggesting that per- haps uniaxial creep tests could provide the needed data more simply and more directly than the IDT creep test. However, it should be kept in mind that in order to properly analyze IDT creep data, it is essential to determine strains in both the verti- cal and horizontal directions, so that calculation of Poisson’s ratio is an inherent part of the IDT procedure. Coefficient of Thermal Contraction The thermal stress developed when a pavement cools is directly proportional to the coefficient of thermal contrac- tion. An equation was developed during SHRP for estimat- ing the coefficient of thermal contraction, which is based upon mixture composition and the coefficient of thermal contraction values for the binder and aggregate (1): where αmix = linear coefficient of thermal contraction for mix- ture, m/m/C; αAC = volumetric coefficient of thermal contraction for asphalt binder, m3/m3/C; αAgg = volumetric coefficient of thermal contraction for aggregate, m3/m3/C; and VMA = voids in mineral aggregate. As detailed by Kwanda and Stoffels, the SHRP equation is not accurate (8). Values of αmix measured by Kwanda and Stoffels and as calculated using the SHRP equation are plotted in Fig- ure 5. Another problem with the SHRP approach is that the coefficient of thermal contraction of the aggregate must be known. The values estimated during SHRP were made using αAgg values estimated based upon typical values for the aggre- gates used in each mixture. In most cases, this information will α α α mix AC AggVMA VMA = + −( )100 300 1( ) 1.0E-05 2.0E-05 3.0E-05 1.0E-05 2.0E-05 3.0E-05 Measured Mix Alpha, m/m/C SH RP M ix Al ph a, m /m /C Figure 5. Coefficient of thermal contraction values for SHRP mixtures, as measured by Kwanda and Stoffels (8) and as predicted using the SHRP equation.

not be readily available to engineers and technicians perform- ing mixture design and analysis. Although laboratory proce- dures for measuring the coefficient of thermal contraction of asphalt concrete mixtures do exist, these methods have not been widely used and are of unknown precision (9). An improved, simpler approach is needed for estimating αmix for use in analyzing low-temperature IDT and/or uniaxial creep and strength test data. In examining the thermal contraction data on the SHRP mixtures for this project, it was found that the mixture coeffi- cient of thermal contraction as predicted using the SHRP equa- tion is largely independent of αAgg. This is because the coefficient of thermal contraction for binders—typically around 1.15 × 10−4 m/m/°C (linear) at temperatures above the glass transition—is much, much larger than the typical value for construction aggregates, about 7 × 10−6 m/m/°C. Further- more, it was found that mixture coefficient of thermal con- traction was much more strongly related to binder volume rather than VMA, as assumed in the SHRP equation. There- fore, a more appropriate equation for estimating the coeffi- cient of thermal contraction for asphalt concrete mixtures would be: Where Vbe is the volume percentage of asphalt binder in a mixture, and the coefficient of thermal contraction for the binder is a linear value, in m/m/°C. Equation 2 can be re- arranged to give αAC in terms of the mixture composition and coefficient of thermal contraction: Using Equation 3, the SHRP mixture composition data pro- vided by Lytton and his associates (1), and the mixture coeffi- cient of thermal contraction values measured by Kwanda and Stoffels (8), αAC values were estimated for the SHRP mixtures. Because coefficient of thermal contraction values for binders are largely a function of the glass transition temperature of the binder, there should be an approximate relationship between binder stiffness at low temperature and this estimated value of αAC. However, the binder data on the SHRP mixtures were very limited and based on measurements on extracted binders that are probably not highly reliable. Also, low- temperature binder data might not always be available when analyzing data on asphalt concrete mixtures at low tempera- ture. Therefore, it was felt that mixture stiffness data would provide a more practical means of estimating αAC. Mixture creep compliance is a function of binder stiffness, aggregate modulus, and mixture composition, and so is not a good choice for relating to binder coefficient of thermal contraction. Mix- ture m-value (d [log (D)]/d [log(t)]), where D is the creep com- pliance, is a much better choice for correlation to αAC, because this should be largely independent of aggregate properties and mixture composition. Figure 6 is a plot of αAC values calcu- α α AC mix VMA Vbe= − × −( )−100 7 10 100 3 6 ( ) α α mix ACVbe VMA = + × −( )−7 10 100 100 2 6 ( ) 14 lated using Equation 3 as a function of mixture m-values. There is a definite relationship, though it is only weak to moderate in strength (R2 = 42 %). However, it should be kept in mind that the measurement of the coefficient of thermal contraction of the mix is difficult and somewhat variable. The standard deviation for αmix for the data reported by Kwanda and Stoffels (8) was 1.5 × 10−6 m/m/°C, corresponding to a standard error (n = 2) of 1.1 × 10−6 m/m/°C and a d2s precision of 3.0 × 10−6 m/m/°C. For the average αmix value of 2.0 × 10−5 m/m/°C, this last value corresponds to a precision of 15 percent as a percent- age of the mean response. Also note in Figure 6 that the cal- culated values of αAC are relatively large, typical for tem- peratures above Tg. It can be concluded that it is generally not necessary to account for the decrease in αAC that occurs at and below Tg. Using the relationship shown in Figure 6, αAC values were estimated for the SHRP mixtures and then used along with Vbe and VMA values to predict αmix values, using Equation 2. These calculations can be combined into one equation for estimating the coefficient of thermal contraction of asphalt concrete mixtures: Where m is the log-log slope of the mixture creep compli- ance with respect to time (t), from = 5 to 100 seconds at the lowest test temperature, normally −20°C. The resulting val- ues are compared to those measured by Kwanda and Stoffels (8) in Figure 7. Although the predictions are not highly accu- rate, they are substantially better than those made using the SHRP equation (Figure 5). Furthermore, compared with the d2s confidence limits for measured αmix (included in Figure 7 as horizontal error bars), the accuracy of the predictions is probably as good as can be expected and appears to be com- parable in accuracy to values determined experimentally. It is suggested that Equation 4 be used to estimate αmix values when analyzing low-temperature creep and strength data on αmix m Vbe VMA = × + ×( ) + × −( ) − − − 5 3 10 7 7 10 7 10 100 100 4 4 5 6 . . ( ) y = 5.34E-04x + 7.72E-05 0.0E+00 5.0E-05 1.0E-04 1.5E-04 2.0E-04 2.5E-04 0.00 0.05 0.10 0.15 0.20 Mix m at -20 C Ca lc . Bi n de r A lp ha , m /m /C Figure 6. Calculated binder coefficient of thermal contraction as a function of mixture m-value at −20°C for SHRP mixtures (R2 = 42%).

15 asphalt concrete mixtures, rather than either using the SHRP equation (Equation 1) to estimate values or deter- mining values experimentally. Estimation of Relaxation Modulus from Creep Compliance Another potential problem in the analysis of low- temperature creep data is the estimation of relaxation modu- lus from creep compliance. This is an essential step in the calculation of thermal stress in a pavement using either IDT or uniaxial creep data. In the approach developed by Roque and his associates during and after SHRP (1,5), a master curve of creep compliance is developed from creep data at three tem- peratures, normally −20, −10 and 0°C. Then, an exponential, or Prony, series is fit to these data: where D(tr) = creep compliance at reduced time tr, D0 = glassy compliance at tr = 0, Di = compliance for Prony series element i, τi = relaxation time for Prony series element i, and η = viscosity as tr → ∞. The relaxation modulus is related to the creep compliance through the Laplace transform: where L[D(t)] = the Laplace transform of the creep compliance, L[E(t)] = the Laplace transform of the relaxation modulus, and s = the transform parameter. An exponential series for the relaxation modulus can be cal- culated once the Prony series parameters for the creep com- pliance are known: L D t L E t s( )[ ] ( )[ ] = 2 6( ) D t D D e tr i tr i i N r( ) = + −( ) +− = ∑0 1 1 5τ η ( ) where E(tr) = relaxation modulus at reduced time tr Ei = modulus for Prony series element i τi = relaxation time for Prony series element i Both Equation 5 and Equation 7 represent mechanical ana- logues for describing linear viscoelastic behavior. Equation 5 represents a generalized Maxwell model, whereas Equation 7 represents a generalized Kelvin model. The procedure described above was used to calculate relax- ation modulus using data for six different mixtures, as sub- mitted by Lab L4 of the IDT creep precision study described previously. In fitting the Prony series to the creep compli- ance data, five evenly spaced relaxation times were assumed, covering a time range slightly larger than that for the entire master curve. Then the compliance values for each element were determined using simultaneous equations, resulting in exact agreement between the measured and fitted Prony- series compliance values at each of the selected relaxation times. The Prony series parameters for the relaxation mod- ulus were calculated using the collocation method described by Christensen (17); a detailed description of this method is beyond the scope of this report, but it also relies on simultane- ous equations to determine the series parameters. An example of the Prony series fit to the creep compliance is shown in Figure 8, which is for mixture 1 from Lab L4 of the precision study. Note that the compliance values predicted by the Prony series approach diverge dramatically from the power law fit to the master curve at a reduced time of about 1 × 106 seconds. This represents the end of the experimentally determined mas- ter curve and the longest relaxation time for the Prony series. Figure 9 shows the corresponding predicted relaxation modu- lus; the creep modulus, 1/D(t), which is a rough approximation to the relaxation modulus; and an estimate of the relaxation modulus based upon Christensen’s method for approximate inversion of the Laplace transform (10,17). As with the creep compliance, the relaxation modulus values predicted using the Prony series approach diverge dramatically from other esti- mates at long reduced times. Some irregularities in the Prony series values are also evident as waviness in the master curve at long reduced times, which is due to the discrete nature of the Prony series. If a very large number of elements are used at closely spaced relaxation times, these irregularities become insignificant. It would appear from this and other comparisons that Christensen’s approximate method is somewhat more accurate and reliable than the Prony series method, although the differences are small except at long reduced times. The six mixtures submitted by Lab L4 in the precision study were analyzed as described above. Furthermore, each analy- sis was performed using the full set of creep data (−20, −10, and 0°C data), using data at −20 and −10°C only, and using data at −20°C only. This was done to evaluate the effect of mixture stiffness on the Prony series error, because the error E t E er i i t i N r( ) = − = +∑ τ 1 1 7( ) 1.0E-05 2.0E-05 3.0E-05 1.0E-05 2.0E-05 3.0E-05 Pr ed ic te d  m ix , m /m /C Measured mix, m/m/C Figure 7. Mixture coefficient of thermal contraction values as measured by Kwanda and Stoffels (8) (with d2s precision limits for measured values) and as predicted by Equation 4.

16 1.E-07 1.E-06 1.E-05 1.E-04 1.E-03 1.E-02 1.E-01 1.E-02 1.E+00 1.E+02 1.E+04 1.E+06 1.E+08 1.E+10 1.E+12 Reduced Time at -20°C, s Co m pl ia nc e, 1 /p si Prony Series Power Law Figure 8. Creep compliance for Mixture 1 from Lab L4 of the precision study: Power law and Prony series fits to the master creep curve. 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 1.E-02 1.E+00 1.E+02 1.E+04 1.E+06 1.E+08 1.E+10 1.E+12 Reduced Time at -20°C, s E( t) or 1/ D( t), ps i E(t) from Prony Series E(t) Approximate 1/D(t) Figure 9. Relaxation modulus for mixture 1 from Lab L4 of the precision study: Values estimated using Prony series approach, Christensen’s approximate method, and the inverse of the creep compliance. is likely to become more severe as the mixture becomes stiffer. The results shown above were typical, and the analysis con- firmed that the extent of this error became larger as the asphalt concrete stiffness increased. To quantify the magnitude of this error, Christensen’s version of the SHRP analysis method was used to estimate a critical cracking temperature (10). This method is essentially identical to the SHRP method, but Christensen’s (17 ) approximate method for estimating relax- ation modulus from creep compliance is used rather than the Prony series approach, and the calculation stops at estimat- ing the critical cracking temperature, Tc, defined as that at which the thermal stress in the pavement reaches the tensile strength. In this case, a typical mixture coefficient of thermal expansion of 1.1 × 10−5 m/m/°C was assumed for all mixtures. Similarly, a typical tensile strength of 3.0 MPa was also assumed. However, to estimate the potential error in the Prony series approach, three additional estimates of Tc were made using relaxation modulus values estimated using the Prony series approach, with full data, data to −10°C, and with −20°C data only. The results of this analysis are summarized in Fig- ure 10. Note that the critical cracking temperatures estimated using the Prony series approach are always lower than those calculated using Christensen’s (17) approximate method for estimating the relaxation modulus. Furthermore, the error increases as the data used in the analysis become stiffer. The errors however are generally small—only a few degrees— though for the −20°C data, the errors often exceed 3°C. This error can be corrected in several ways. The number of relaxation times used in the Prony series could be increased (say doubled) and the time covered by the Prony series also increased. Another approach would be to use an approxi- mate method for estimating the relaxation modulus, which,

17 although not as theoretically elegant, produces more robust estimates over a wide range of conditions. The third approach is the simplest and most direct: adjust IDT (or uniaxial) creep test temperatures to avoid collecting exceedingly stiff com- pliance data. Based upon this analysis and general experience with low-temperature creep data, the following protocol is suggested: • For mixtures made using PG XX-22 and PG XX-28 binders, creep tests should be performed at −20, −10 and 0°C; tensile strength should be determined at −10°C. • For mixtures made using PG XX-34 binders (or softer), creep tests should be performed at −30, −20 and −10°C; strength tests should be performed at −20°C. • For mixtures made using PG XX-16 binders (or harder), or severely aged mixtures, creep tests should be per- formed at −10, 0, and +10°C; strength tests should be performed at 0°C. This approach should ensure that the compliance data col- lected will not be prone to excessive errors when the maxi- mum relaxation time for the Prony series is exceeded. This will have the added benefit of producing more uniform data, which should help improve the precision of the test. This pro- tocol is also consistent with that presented earlier, based on more practical considerations. Summary and Findings on Theory of Testing and Analysis Under the loads normally used in the IDT creep test and likely to be used for uniaxial creep testing, asphalt concrete behaves essentially as a linear viscoelastic material. Data at this time suggest that IDT specimens are large enough to provide for a reasonable degree of homogeneity for most asphalt concrete mixtures, though additional research needs to be done in this area. Poisson’s ratio does not need to be known for an analysis of thermal stresses in asphalt concrete pavement, so there is no need to determine it as part of a uniaxial creep test. It is, however, an essential part of the IDT creep test. The SHRP equation for estimating the coefficient of ther- mal expansion of asphalt concrete mixtures is not accurate. A simple and reasonably accurate alternative method has been developed that uses the volumetric composition of the mixture and the mixture m-value (log-log creep compliance slope with respect to time) to estimate the coefficient of thermal contrac- tion of the mixture. This approach appears to be similar in accuracy to the laboratory measurement of the coefficient of thermal contraction. The Prony series method of calculating relaxation modulus from creep compliance, in general, works acceptably well, but can result in significant errors for stiff mixtures when the max- imum relaxation time for the series is exceeded during the analysis. To avoid this problem, test temperatures should be varied according to the binder grade used in producing a mix- ture. The current test temperatures should continue to be used for PG XX-22 and PG XX-28 binders. For mixtures made using softer binders, all test temperatures should be lowered by 10°C; for mixtures made using harder binders or heavily aged binders, all test temperatures should be raised by 10°C. COMPARISON OF COMPLIANCE VALUES AS DETERMINED USING UNIAXIAL TENSION, UNIAXIAL COMPRESSION, AND THE IDT TEST An experimental test program was designed and executed to answer several important questions related to the determi- nation of the low-temperature creep compliance of asphalt concrete mixtures: • Is the low-temperature creep compliance of asphalt con- crete similar in tension and compression? • Does the IDT creep test provide creep values similar to those determined in uniaxial tension or compression? • If the creep compliance values as determined in uniaxial tension, uniaxial compression, and with the IDT creep test are not similar, what is the nature of the relationship among these data? • How does the precision of test data compare for compli- ance determined using uniaxial tension, uniaxial com- pression, or the IDT test? This section of this report discusses the design, execution, results, and findings of this test program. Materials, Methods, and Experiment Design Table 8 lists the four aggregate types and gradations used in the laboratory testing performed as part of Phase III of NCHRP Project 9-29. Nominal maximum aggregate size ranged from 9.5 mm to 25 mm, and the mineralogy was -40 -30 -20 -10 0 4-1 4-2 4-3 4-4 4-5 4-6 Mix Code Cr iti ca l P av em en t T em p. , C Tc Prony 0°C Prony -10°C Prony -20°C Figure 10. Errors in critical cracking temperature resulting from using Prony series approach to estimate relaxation modulus.

distinctly different for each aggregate type. The four binders used in the study are given in Table 9. The grades included were PG 58-28, PG 64-22, PG 76-16, and PG 76-22. The first three of these asphalt binders were unmodified; the PG 76-22 was an SBS modified binder. A total of 16 mixtures were designed with these materials— each of four aggregate types with each of four binder types. All were designed according to Superpave procedures, with an Ndesign of 100 gyrations. The resulting design volumetric com- position of the mixtures is given in Table 10 (the design air void level was in all cases 4 percent by volume). The resulting mixtures covered a wide range of VMA—12.6 to 17.6 per- 18 cent by volume—and a similarly wide range of VFA—68 to 77 percent by volume. The experiment consisted of measuring both the creep com- pliance and tensile strength of the mixtures at low temperature, using various procedures. The creep compliance was mea- sured by indirect tensile, uniaxial tension, and uniaxial com- pression. The IDT creep compliance tests were performed fol- lowing procedures outlined in AASHTO T322. Specimens having a diameter of 150 mm and a thickness of 50 mm were sawn from standard Superpave gyratory specimens. The spec- imens for uniaxial tension and uniaxial compression tests were 100 mm in diameter and 150 mm high and were cored and sawn from high (165-mm) gyratory specimens. The procedure used in the uniaxial tests followed as much as possible the same protocol as described in AASHTO T322 for IDT tests, except where the different geometry made changes necessary. The LVDTs used in the IDT creep tests were as described in AASHTO T322—two transducers on each face, one vertical and one horizontal, all with a gage length of 37.5 mm. For the uniaxial tests, two LVDTs were mounted in diametrally oppo- site locations at the specimen midheight with a gage length of 100 mm. For the uniaxial tension test, the ends of the specimen were fastened to the loading platens using epoxy cement. For the compression tests, rubber loading pads were used between the specimen ends and platens to distribute the load and avoid stress concentrations. All creep tests were 100 seconds in dura- tion and were performed at three temperatures for each mix- ture. Most of the specimens were tested at −20, −10 and 0°C. Specimens made with the PG 76-16 binder were however tested at −10, 0 and 10°C, because of the hardness of the binder used in specimens (as recommended previously). Two types of strength tests were performed: IDT strength, per AASHTO T322, and uniaxial tension. The tests were per- formed at the middle creep temperature, usually −10°C, except that the specimens with the PG 76-16 binder were tested at 0°C. The IDT strength tests were instrumented so that the exact procedure described in AASHTO T322 could be used to determine the point of failure. In analyzing the data, this pro- cedure was used along with the more direct approach of sim- ply using the maximum load to determine the IDT strength. Hereafter, these are referred to as the corrected IDT strength Binder Grade PG 58-28 PG 64-22 PG 76-16 PG 76-22 Temperature °C Stiffness (MPa)/m-value (PAV Residue): 78/ -6 0.321 214/ 158/ 179/ -12 0.359 0.285 0.349 216/ 507/ -18 0.373 0.275 548/ -24 0.278 Aggregate Type: 9.5-mm VA Limestone 12.5-mm MD Diabase 19-mm VA Granite 25-mm PA Gravel Sieve Size mm Percent Passing by Weight: 37.5 100 100 100 100 25.0 100 100 100 97 19.0 100 100 96 86 12.5 100 97 76 63 9.5 97 75 54 46 4.75 63 38 33 35 2.36 42.0 29.3 24.0 25.0 1.18 26.7 22.7 18.8 14.0 0.600 17.2 18.5 15.0 9.0 0.300 11.2 11.9 10.8 5.0 0.150 7.9 7.2 6.1 4.0 0.075 6.3 5.6 3.2 3.9 TABLE 8 Aggregate gradations TABLE 9 Binder grades and bending beam rheometer test data Aggregate Type: Binder Property VA Limestone MD Diabase VA Granite PA Gravel AC, Wt. % VMA, Vol. % PG 58-28 VFA, Vol. % AC, Wt. % VMA, Vol. % PG 64-22 VFA, Vol. % AC, Wt. % VMA, Vol. % PG 76-16 VFA, Vol. % AC, Wt. % VMA, Vol. % PG 76-22 VFA, Vol. % 6.2 4.75 4.4 4.4 17.3 13.7 14.3 12.6 76.9 70.7 72.1 68.2 6.2 4.75 4.4 4.4 17.3 13.5 14.2 12.6 76.9 70.5 71.7 68.3 6.2 4.75 4.4 4.4 17.6 13.7 15.0 12.8 77.2 70.8 73.3 68.8 6.2 4.75 4.4 4.4 17.0 13.5 14.4 12.7 76.5 70.3 72.1 68.6 TABLE 10 Volumetric properties of mixtures

19 and the uncorrected IDT strength. The IDT strength tests were performed using a loading rate of 12.5 mm per minute. The uniaxial tension strength tests were performed at a load- ing rate of 3.75 mm/min, which provides a strain rate roughly equivalent to that in the standard IDT strength test. The experiment designs for both creep and strength can be considered full factorials. For the creep experiment, there are five factors—test type, aggregate type, binder type, temper- ature, and loading time—at 4, 4, 3, and 2 levels, respectively (loading times analyzed were 10 and 100 seconds). For the strength experiment, there are only three factors—test/analysis type, aggregate type, and binder type—at 3, 4, and 4 levels, respectively. As described in the following section, a variety of graphical and statistical methods were used in analyzing the data. The primary problem in both experiments involved comparing test data produced on the same set of materials using different methods of testing. Many of the comparisons were done using regression analysis, often with log-log trans- formations. A more rigorous comparison of compliance test data was done by treating compliance values as paired mea- surements. For both sets of tests, estimates were made of test variability, presented as both standard deviation and coefficient of variation. Results of Low-Temperature Creep Compliance Experiment The most straightforward comparison of data involves graphical methods and basic regression analysis. In Figure 11, the compliance as measured in uniaxial compression is com- pared to that measured in uniaxial tension. As might be expected, the compliance in tension is usually higher than that measured in compression. The difference between these two measurements is smaller at low temperatures/low compli- ance values and increases at higher temperatures/compliance values. At high compliance values, the value in tension is often two or more times the value as determined in compression. There is no obvious trend in terms of aggregate—the relation- ship between the two tests appears to be similar for the four different aggregates used. In Figure 12, the compliance values measured in uniaxial tension are compared to those determined using the IDT pro- cedure. The compliance values in tension again appear to be significantly higher, exhibiting a very similar relationship to that between compliance in uniaxial tension and compression. However, in this case it appears that the nature of the relation- ship varies slightly among the different aggregates used. The difference in compliance values appears largest for the Vir- ginia limestone mixtures, whereas the difference for the Vir- ginia granite mixtures appears to be negligible. This suggests that the compliance as measured using the IDT can be affected by the aggregate used; it is possible, for example, that because of the high stresses at the point of loading that some aggregate particles are being crushed, resulting in substantial redistribu- tion of stresses. It is also possible that the anisotropy is in fact caused by preferential orientation of asymmetric aggregate particles and that the degree of such orientation varies depend- ing upon the specific aggregate used in a mixture. Based upon Figures 11 and 12, it should be expected that the compliance as measured in uniaxial compression and as mea- sured using the IDT procedure will compare closely. This is confirmed in Figure 13, where these values are plotted against one another. Note that this relationship appears to vary depend- ing on aggregate type, with the softer aggregates exhibiting somewhat lower compliance values in the IDT test compared to the harder aggregates (the Maryland aggregate is a relatively y = 4.24x1.08 R2 = 90 % 1.E-07 1.E-06 1.E-05 1.E-04 1.E-07 1.E-06 1.E-05 1.E-04 Compliance, Compression, 1/psi Co m pl ia n c e ,T en si o n , 1 /p si MD DBASE PA GRVL VA GRNT VA LMSTN Equality Figure 11. Comparison of compliance as measured in uniaxial compression and as measured in uniaxial tension. y = 4.48x1.08 R2 = 86 % 1.E-07 1.E-06 1.E-05 1.E-04 1.E-07 1.E-06 1.E-05 1.E-04 Compliance, IDT, 1/psi Co m pl ia n c e ,T e n s io n , 1/ ps i MD DBASE PA GRVL VA GRNT VA LMSTN Equality Figure 12. Comparison of compliance as measured in uniaxial tension and as measured using IDT test. y = 0.857x R2 = 93 % 1.E-07 1.E-06 1.E-05 1.E-04 1.E-07 1.E-06 1.E-05 1.E-04 Compliance, Compression, 1/psi Co m pl ia n c e , ID T, 1/ ps i MD DBASE PA GRVL VA GRNT VA LMSTN Equality Figure 13. Comparison of compliance as measured in uniaxial compression and as measured using IDT test.

hard diabase). To confirm this, Figure 14 is shown, which is identical to Figure 13, but only includes the hard aggregates (Virginia granite and Maryland diabase). Although the regres- sion line is slightly closer to equality, and the R2 value is actu- ally lower, the relationship appears to be more uniform and indicative of a better relationship between these test data. Because of the possibility of crushing aggregate and the result- ing non-linear behavior, caution should be used in applying the IDT test to mixtures made using soft, friable aggregates. Two findings stand out in the graphical comparison of compliance values: (1) compliance values in tension and compression are not equal, as assumed in the analysis of the IDT test; and (2) compliance values as determined using the IDT procedure tend to agree very well with those determined in uniaxial compression but not with values determined using uniaxial tension. In interpreting these findings, it must be remembered that the axes in which compliance is determined in these three tests are not the same—the uniaxial tests eval- uate compliance along the length (or height) of the gyratory specimen, whereas the IDT evaluates compliance along the diameter of the specimen. Furthermore, the air void distribu- tion in typical gyratory specimens is not uniform, but tends to be higher near the center of the specimen. Because the strain measurements in the IDT test are made near the center of the specimen, the effective air void content for the IDT tests is lower than that for the uniaxial tests. Therefore, there are two possible sources for the higher compliance values de- termined in the IDT test compared to uniaxial tension: anisotropy and differences in air void content. It is possible that the orientation of aggregate particles during compaction causes anisotropy in laboratory compacted specimens, so that the compliance along the specimen diameter—as deter- mined with the IDT test—is lower than as determined in uni- axial tests. The somewhat lower effective air void content in the IDT specimens is also expected to produce lower compli- ance values. However, an analysis of creep modulus values as predicted using the Hirsch model (4) indicates that differences in air void levels probably only account for a few percent of the observed differences. Because of the apparent presence of substantial anisotropy in asphalt concrete specimens, the IDT creep test should be retained as the preferred procedure for 20 characterizing the low-temperature stiffness of asphalt con- crete mixtures. A more rigorous comparison of data generated by the three low-temperature test methods is given in Tables 11 through 16, which summarize the result of statistical pair-wise compar- isons for creep compliance, master curve parameters, and critical cracking temperature. Table 11 compares the compli- ance measured in uniaxial compression and uniaxial tension. This table includes comparisons at loading times of 10 and y = 0.897x R2 = 88 % 1.E-07 1.E-06 1.E-05 1.E-04 1.E-07 1.E-06 1.E-05 1.E-04 Compliance, Compression, 1/psi Co m pl ia n c e, ID T, 1/ ps i MD DBASE VA GRNT Equality Figure 14. Comparison of compliance as measured in uniaxial compression and as measured using IDT test, hard aggregates only. Parameter D(Comp.) 1/psi D(Tens.)– D(Tens.)– D(Comp.) % Test Stat. |t*| Sig. Diff.? Temp. 1, 10 s 1.08E-07 19.3 2.228 YES Temp. 1, 100 s 1.01E-07 9.9 1.295 NO Temp. 2, 10 s 3.76E-07 30.6 2.559 YES Temp. 2, 100 s 5.29E-07 23.4 2.126 NO Temp. 3, 10 s 1.26E-06 34.5 2.175 YES Temp. 3, 100 s 2.16E-06 23.4 1.773 NO TABLE 11 Statistical test for equality of compliance measured in uniaxial compression and as measured in uniaxial tension Parameter Diff.: Tens. – Comp. Test Stat. |t*| Sig. Diff.? Log (D0) 0.093 1.574 NO Log (D1) 0.260 2.125 NO M -0.094 3.345 YES d log a(T)/d T -0.038 3.584 YES TABLE 12 Statistical test for equality of master curve parameters and critical temperatures from uniaxial compression data and uniaxial tension data Parameter D(IDT) – D(IDT) – D(Tens.) 1/psi D(Tens.) % Test Stat. | t*| Sig. Diff.? Temp. 1, 10 s -1.69E-07 -50.0 2.787 YES Temp. 1, 100 s -1.98E-07 -45.6 2.053 NO Temp. 2, 10 s -4.58E-07 -74.9 2.677 YES Temp. 2, 100 s -5.98E-07 -51.7 2.188 YES Temp. 3, 10 s -1.54E-06 -102.4 2.260 YES Temp. 3, 100 s -2.42E-06 -55.4 1.766 NO TABLE 13 Statistical test for equality of compliance measured in uniaxial tension and as measured using the IDT procedure Parameter Diff.: IDT – Tens. Test Stat. |t*| Sig. Diff.? Log (D0) -0.201 2.117 NO Log (D1) -0.308 2.345 YES M 0.123 3.417 YES d log a(T)/d T 0.046 3.597 YES TABLE 14 Statistical test for equality of master curve parameters and critical temperatures from uniaxial tension data and IDT data

21 100 seconds at all three test temperatures. The paired obser- vation test is constructed as follows (18): Where Y1 and Y2 are the two quantities being compared, for example, compliance at the lowest temperature and 100 sec- onds as determined using compression (Y1) and tension (Y2); and s is the pooled standard deviation. From the results sum- marized in Table 11, it appears that the difference between compliance measurements made in compression and tension is greater at short loading times than at long loading times, although the compliance as determined in tension is always greater than that determined in compression. Table 12 shows that several of the master curve parameters exhibit significant differences. The master curve parameters included in Table 12 (and Tables 14 and 16) are D0, the glassy compliance; D1, the location parameter; M, the limiting log-log slope of the com- pliance function; and the shift constant, d log a(T)/d(T) (the slope of the log of the shift factor with respect to temperature). Tables 13 and 14 are the corresponding summary compar- isons of compliance as measured in uniaxial tension and as determined using the IDT procedure. In this case, the differ- ences appear even larger, with most compliance values and most master curve parameters showing statistically signifi- cant differences for the two procedures. Note that the differ- ences in compliance values range from about 45 percent to over 100 percent, with the compliance in tension always much larger than that determined using the IDT test. H Y Y H Y Y t t n H H t Y Y s Y Y a a 0 1 2 1 2 0 1 2 1 2 1 2 1 : : ; ; = ≠ ≤ − −( ) = −( ) −( ) If conclude otherwise,conclude   α The final set of statistical comparisons is given in Tables 15 and 16. In examining the compliance values, the difference between compliance values determined in uniaxial compres- sion and using the IDT test is statistically significant in two of six cases. The compliance values determined in compression range from about 8 to 20 percent higher than those determined using the IDT test. The only master curve parameter for which the difference is statistically significant is the shift constant. In general, the compliance values determined using the IDT test and those determined using uniaxial compression com- pare favorably, but they are not entirely interchangeable. The statistical analysis presented above agrees with the graphical comparison presented earlier and confirms that the observed differences in compliance values determined using the three procedures are statistically significant. As discussed, the IDT creep compliance values are the lowest, followed by the values determined in compression. The com- pliance values determined in tension are the highest. As dis- cussed earlier, the relatively low compliance values determined using the IDT test are probably the result of anisotropy and not, primarily, differences in air void, air void distribution, or both. An important consideration in evaluating the three low- temperature compliance tests is the variability in the resulting data. To provide better estimates of variances, the data from all mixtures were combined into two sets having reasonably sim- ilar compliance values. The lower compliance set included data from all mixtures for temperature 1 at 100 seconds and temperature 2 at 10 seconds. The higher compliance set included data from all mixtures for temperature 2 at 100 sec- onds and temperature 3 at 10 seconds. By combining the data in this way, 30 degrees of freedom were achieved in the vari- ance estimates. The resulting variances are shown in Table 17. By calculating variance ratios for each pair of data, an F-statistic was constructed and compared to a critical value of F(1 − α/2, n1 − 1, n2 − 1) = F(0.975, 30, 30) = 2.07 (18). At a significance level of 0.05, only the difference between the variances for the IDT test and the compression for the lower compliance set is statistically significant. In general, it appears that the three test procedures produce data with sim- ilar variability. The pooled C.V. for the compliance values were 10 percent for uniaxial tension, 16 percent for uniaxial compression, and IDT for n = 1 replicate. For n = 2 replicates, the C.V. values were 7 percent for uniaxial tension and 11 per- cent for uniaxial compression and IDT. The C.V. dropped further for n = 3 replicates to 6 percent for uniaxial tension and 9 percent for uniaxial compression and IDT. Parameter D(Comp.) 1/psi D(IDT)–D(IDT)– D(Comp.) % Test Stat. |t*| Sig. Diff.? Temp. 1, 10 s -6.10E-08 -16.5 1.973 NO Temp. 1, 100 s -9.71E-08 -21.2 2.200 YES Temp. 2, 10 s -8.21E-08 -14.6 2.130 NO Temp. 2, 100 s -6.90E-08 -8.2 1.284 NO Temp. 3, 10 s -2.85E-07 -20.6 2.394 YES Temp. 3, 100 s -2.66E-07 -8.3 1.205 NO TABLE 15 Statistical test for equality of compliance measured in uniaxial compression and as measured using the IDT procedure Parameter Diff.: IDT – Comp. Test Stat. |t*| Sig. Diff.? Log (D0) -0.108 1.434 NO Log (D1) -0.047 0.627 NO M 0.029 1.436 NO d log a(T)/d T 0.008 2.140 YES TABLE 16 Statistical test for equality of master curve parameters and critical temperatures from uniaxial compression data and IDT data Test Lower Compliance Temp. 1, 100 s & Temp. 2, 10 s Higher Compliance Temp. 2, 100 s & Temp. 3, 10 s Tension 7.53E-15 8.74E-14 Compression 1.52E-14 8.16E-14 IDT 6.95E-15 6.67E-14 TABLE 17 Estimated variances for compliance measurements

Comparison of Strength Test Procedures An important aspect of the IDT creep and strength test procedure is the specific procedure required to perform the IDT strength test. As currently written, the IDT strength test in AASHTO T322 requires deformation to be monitored using vertical and horizontal LVDTs mounted on the specimen. The load for calculating strength is determined from the point at which the vertical minus horizontal deformation is a maxi- mum. Unfortunately, this procedure often results in damaged or destroyed transducers. As a result, many laboratories now run the IDT strength test without LVDTs and simply use the maximum load to calculate the strength. One of the main objectives of the experimental plan was to evaluate the differ- ences among the uncorrected IDT strength determined from the maximum load, the corrected IDT strength determined from the maximum difference in the vertical and horizontal deformations, and the strength as measured in direct tension. Figure 15 shows the relationship between uncorrected and corrected IDT strengths. The relationship is reasonably good, with an R2 value of 74 percent. An important, related question is whether or not the correct strength actually provides tensile strength values similar to those measured in direct tension. Figure 16 illustrates the rela- tionship between uncorrected IDT strength and the direct ten- sion strength. Figure 17 is the corresponding plot for corrected IDT strength and strength in the direct tension test. It is clear that the procedure in AASHTO T322 does in fact provide a better estimate of the tensile strength measured in direct tension than using the maximum load in the IDT test to calculate strength. However, the relationship is still not very strong, with an R2 value of 49 percent. It should be remem- bered that asphalt concrete stiffness is anisotropic and that strength might also be so. Therefore, differences in IDT and uniaxial tensile strength are not necessarily indicative of inaccuracies in either test procedure. Although the AASHTO T322 procedure does appear to be reasonable, it is suggested, because of practical problems with this approach, that tensile strength be estimated from uncorrected IDT strength using the equation given in Figure 15 (R2 = 74 %): Tensile Strength IDT Strength = ×( ) +0 78 38 8. ( ) 22 This approach should provide good estimates of actual tensile strength without risking damage or destruction of expensive instrumentation during the IDT strength test. A simple, alternative approach to estimating tensile strength is to develop a regression equation based on mixture volumet- ric composition. Such a method might be useful, for instance, in quality control applications. The best such model found for the data generated in this project is shown in Figure 18, which is a plot of direct tension strength as a function of VFA. This relationship is better than that between IDT strength and tensile strength and similar in strength to that between corrected IDT strength and tensile strength. However, in examining this figure it was noticed that several of the out- lying points were for mixtures made using a modified binder (PG 76-22). A multiple regression model was developed which allowed for a different slope for mixtures with unmodified and mod- ified binders by using an indicator variable for binder type and including in the model the interaction term for indica- tor variable by VFA. The results of this regression model are summarized in Table 18. It was found that if both a differ- ent intercept and slope were allowed for the modified binder, neither term was significant. A different slope was allowed in this case because it was believed to be a more reason- 900800700600500400 900 800 700 600 500 400 300 200 IDT Strength, Uncorrected, psi ID T St re n gt h, Co rr e ct ed , p si R-Sq = 74 % Y = 38 + 0.781X 95% PI 95% CI Reg. Figure 15. Regression line with 95-percent confidence and prediction intervals for relationship between uncorrected and corrected IDT strength. 900800700600500400 800 700 600 500 400 300 IDT Strength (Uncorrected), psi D ire ct T en si on St re ng th , ps i R-Sq = 33 % Y = 285 + 0.336X 95% PI 95% CI Reg. Equality Figure 16. Regression line with 95-percent confidence and prediction intervals for relationship between uncorrected IDT strength and direct tension strength. 800700600500400 800 700 600 500 400 300 Corrected IDT Strength, psi D ire ct T en si on S tre ng th , ps i R-Sq = 49 % Y = 256 + 0.452X 95% PI 95% CI Reg. Equality Figure 17. Regression line with 95-percent confidence and prediction intervals for relationship between corrected IDT strength and direct tension strength.

23 able assumption. Based upon the results given in Table 18, the regression equation for strength of mixtures using non- modified binders is: For mixtures made using modified binders, the equation becomes As seen in Figure 19, this approach greatly improved the quality of the model. In this plot, modified VFA is simply VFA for mixtures with unmodified binders and 1.08 × VFA for mixtures made using modified binders—this adjustment accounts for the difference in slopes for the two cases. Addi- tional research is needed to expand the data set underlying this model, especially with regard to additional modified binders. However, it is potentially a very useful method for estimating tensile strength when measurements are impossi- ble or impractical. Based on this analysis, the procedure included in AASHTO T322 for determining the true point of failure in the IDT strength test produces significantly better estimates of the true tensile strength than simply using the maximum load devel- oped during the test. However, the AASHTO T322 procedure is not highly accurate and can damage the LVDTs used to monitor deformation during the test. It is therefore recom- mended that the standard procedure for determining IDT strength should be to determine the maximum load, calculate the uncorrected IDT strength, and then correct it using Equa- tion 8. For some applications, such as quality control testing, Strength VFA= − +739 18 1 10. ( ) Strength VFA= − +739 16 9 9. ( ) strengths estimated from VFA, using Equations 9 and 10 (or improved versions of these relationships) are probably ade- quate. Additional research should be performed to better define the relationship between mixture volumetrics, binder type, and tensile strength. Effect of Test Procedure on Estimated Cracking Temperature From the previous analyses and discussions, it is clear that there are differences in both creep compliance and strength, depending upon the specific test procedure used. Ultimately, the most important aspect of these differences is their effect on estimated critical cracking temperature. To evaluate the effect of the test procedure on critical cracking temperature, a thermo-viscoelastic analysis was performed using the three different data sets, following Christensen’s version (10) of Roque and Hiltunen’s procedure (5). To limit the effect of dif- ferences in tensile strength, the direct tension tensile strength was used for each analysis. The results of these analyses are shown in Figures 20 through 22. In Figure 20, critical cracking temperature from compli- ance in uniaxial tension is compared to critical temperature determined using compliance data in uniaxial compression. Included in this plot (and the following two) are two standard deviation confidence intervals for the difference between two observations. The agreement in this case is reasonable, except for two points (both Virginia limestone mixes), which show much lower cracking temperatures using tension data than those determined using compression data. The corre- 77767574737271706968 700 600 500 400 300 VFA, Vol. % D ire ct T en si on S tre n gt h, ps i R-Sq = 51 % Y = -708 + 16.8X PI95% CI95% Reg. Figure 18. Regression line with 95-percent confidence and prediction intervals for relationship between VFA and direct tension strength. Predictor Coefficient Standard Deviation t-value Significance Level Constant -739.0 228.8 -3.23 0.007 VFA 16.939 3.171 5.34 0.000 Ind. Varb × VFA 1.1794 0.317 3.72 0.003 R2 = 76.3 %; R2 (adjusted for degrees of freedom) = 72.7 % TABLE 18 Results of regression model for direct tension strength with VFA and binder type as predictors 807570 750 700 650 600 550 500 450 400 350 300 Modified VFA, Vol. % Di re ct T en sio n St re n gt h, ps i R-Sq = 76 % Y = -738 + 16.9X 95% PI 95% CI Reg. Figure 19. Regression line with 95-percent confidence and prediction intervals for relationship between VFA (modified to account for effect of modified binder) and direct tension strength.

-50 -40 -30 -20 -10 -50 -40 -30 -20 -10 Tc (Compression), C Tc (T en si o n ), C MD Diabase PA Gravel VA Granite VA Limestone Equality Figure 20. Comparison of critical temperature determined from creep compliance in uniaxial tension and creep compliance in uniaxial compression (R2 = 55%). -50 -40 -30 -20 -10 -50 -40 -30 -20 -10 Tc (IDT), C Tc (T en si o n ), C MD Diabase PA Gravel VA Granite VA Limestone Equality Figure 21. Comparison of critical temperature determined from creep compliance in uniaxial tension and creep compliance from IDT test (R2 = 42%). -50 -40 -30 -20 -10 -50 -40 -30 -20 -10 Tc (Compression), C Tc (ID T) , C MD Diabase PA Gravel VA Granite VA Limestone Equality Figure 22. Comparison of cracking temperature determined from IDT test and creep compliance in uniaxial compression (R2 = 42%). sponding figure in which critical temperatures were determined using uniaxial tension compliance data and IDT compliance data is shown in Figure 21. In this case, the agreement is poor—there does not appear to be a useful relationship between the results of these analyses. The comparison of crit- ical temperatures determined from IDT compliance data and 24 uniaxial compression compliance data is shown in Figure 22. Again, the relationship is relatively weak. It is somewhat puzzling that the overall differences in com- pliance values for the three procedures do not seem to affect the critical cracking temperatures. For example, because the compliance in uniaxial tension is in general significantly higher than that determined from the IDT test, it would be expected that the critical cracking temperatures determined using uniaxial tension compliance data would, in general, be lower than those determined from IDT data. However, this is not the case, as seen in the previous plots. Apparently, differ- ences in the shapes of the master curves and in the tempera- ture dependence as determined using these procedures tend to offset the trends in differences in compliance. The overall result is that all three methods produce critical cracking tem- peratures in the same temperature range. However, the rela- tionships between critical temperatures are poor. This con- firms that uniaxial compliance test data cannot be used as a substitute for IDT compliance data. Summary and Findings on Comparison of Low-Temperature Creep Compliance Tests and Strength Tests Based upon the results of low-temperature compliance and strength tests performed on 16 different mixtures using several different test procedures, a number of important findings are apparent. Perhaps most importantly, asphalt concrete spec- imens prepared using a gyratory compactor are anisotropic— the compliance determined across the diameter is different from that measured along the length of the cylinder. In gen- eral, it appears that the IDT creep compliance is slightly less than the uniaxial compliance in compression and substan- tially less than the uniaxial compliance determined in tension. Although laboratory compaction using the gyratory device does not exactly replicate field compaction, it seems likely that similar anisotropy exists in pavements. Therefore, caution must be used when comparing compliance or modulus values for asphalt concrete determined using different test geometries and using the resulting values in pavement design. Because of this anisotropy, it is recommended at this time that the IDT creep test be retained as the standard method for measuring low-temperature creep compliance of asphalt concrete. There does not seem to be a similar degree of anisotropy in strength test data. Tensile strengths determined in direct tension are similar to those determined using the corrected IDT strength test procedure in AASHTO T322. Furthermore, it appears that corrected IDT strength can be estimated fairly well from uncorrected IDT strength using Equation 8. Therefore, the overall recommendation from the experimental portion of this study is that the IDT creep and strength test be retained for use in estimating the thermal cracking resistance of asphalt con- crete but that IDT strengths obtained from the maximum load should be empirically adjusted to provide more realistic esti- mates of the actual tensile strengths of mixtures.

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Evaluation of Indirect Tensile Test (IDT) Procedures for Low-Temperature Performance of Hot Mix Asphalt Get This Book
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TRB’s National Cooperative Highway Research Program (NCHRP) Report 530: Evaluation of Indirect Tensile Test (IDT) Procedures for Low-Temperature Performance of Hot-Mix Asphalt evaluates the use of the indirect tensile creep and strength test procedures in American Association of State Highway and Transportation Officials Standard Method of Test T322-03 in mixture and structural design methods for hot-mix asphalt.

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