3.3.5. SX(75) PG 58-34

The flow numbers for the SX(75) PG 58-34 mix varied from 19 to 75, with an average flow number of 47 and standard deviation of 28. As per AASHTO, a mix is considered good for traffic of less than 3 million ESALs if it has a flow number less than 50. The current mix had an average flow number of 47; therefore, this mix is good for traffic of less than 3 million ESALs. However, we had data for only two mixes from the current mix. Therefore, no sensitivity analysis was conducted on this mix.

#### 3.3.6. SX(75) PG 64-22

The flow numbers for the SX(75) PG 64-22 mix varied from 19 to 123, with an average number of 59, median of 49, and standard deviation of 34. As per AASHTO, a mix is considered good for traffic between 3 and 10 million ESALs if it has a flow number greater than 50. The current mix had an average flow number of 59; therefore, this mix is considered good for traffic between 3 and 10 million ESALs. The *t*-test showed the 95% CI boundaries to be 28 and 90. The mix parameters show that mixes with similar properties have statistically different flow numbers. For example, mixes with the prefix 19935 have the same binder supplier, aggregate source, region, and volumetric properties, though they have statistically different flow numbers.

#### 3.3.7. SX(75) PG 64-28

The flow numbers for the SX(75) PG 64-28 mix varied from 32 to 311, with an average number of 106, median of 41, and standard deviation of 118. As per AASHTO, a mix is considered good for traffic between 3 and 10 million ESALs if it has a flow number greater than 50. The current mix had an average flow number of 99; therefore, this mix is considered good for traffic between 3 and 10 million ESALs. The same observations were noted for binders SX(75) PG 58-28 and SX(75) PG 58-34.

#### 3.3.8. SX(100) PG 58-28

Only a single sample with a flow number of 128 was tested for this mix. No statistical test or sensitivity analysis was conducted on this mix due to insufficient data.

#### 3.3.9. SX(100) PG 64-22

The flow numbers for the SX(75) PG 64-22 mix varied from 23 to 388, with an average number of 112, median of 97, and standard deviation of 92. As per AASHTO, a mix is considered good for traffic between 3 and 10 million ESALs if it has a flow number greater than 50. The current mix had an average flow number of 112; therefore, this mix is considered good for traffic between 3 and 10 million ESALs. Nonetheless, a *t*-test was conducted, and the results showed the 95% CI boundaries to be 59 and 164. The mix parameters show that mixes with different properties had statistically similar flow numbers. On the other hand, mixes by the same contractor with the same aggregate source had statistically different flow numbers.

#### 3.3.10. SX(100) PG 64-28

The flow numbers for the SX(100) PG 64-28 mix varied from 77 to 531, with an average of 241, median of 215, and standard deviation of 131. As per AASHTO, a mix is considered good for traffic between 10 and 30 million ESALs if it has a flow number greater than 190. The current mix had an average flow number of 240; therefore, this mix is considered good for traffic between 10 and 30 million ESALs. The *t*-test showed the 95% CI boundaries to be 134 and 347. Three mixes were not statistically the same; however, two mixes had similar properties to the statistically similar mixes. Therefore, flow numbers can be statistically different for the same mix by the same contractor.

## 3.3.11. SX(100) PG 76-28

The flow numbers for the SX(100) PG 76-28 mix varied from 82 to 6343, with an average number of 1578, median of 810, and a standard deviation of 1837. As per AASHTO, a mix is considered good for traffic greater than 30 million ESALs if it has a flow number greater than 740. Although the average flow number was 1482, nearly half of the samples had a flow number less than 740. Therefore, it is very difficult to conclude whether this mix is considered good for traffic greater than 30 million ESALs. Comparing this result with those for the previous binders, the flow number increased with an increase in the high-temperature grade of the binder. Similar observations were noted for the SX(75) mix. The *t*-test showed the 95% CI boundaries to be 893 and 2262. Out of 33 specimens, only 7 specimens were within the 95% CI boundaries.

#### *3.4. Analysis Summary*

The flow numbers for each group and their variations, 95% CI boundaries, etc., are presented in Table 4 and Figure 5. They show that SX(75) PG 58-34 had the lowest flow number and SMA PG 76-28 had the highest flow number. Comparing the average flow numbers with the above-listed values, the following may be concluded:



**Table 4.** Groupwise average flow numbers with 95% boundaries.

The sensitivity analysis summary presented in Table 5 shows that the effects of *Vbe*, *Va*, VMA, VFA, and AC on the flow number are inconsistent. For example, six mixes show that the flow number increases with *Vbe*, two mixes show the opposite, and one mix shows it is insensitive to *Vbe*. This inconsistency is true for *Va*, VMA, VFA, and AC as well. The reason behind this may be the effects of the paving contractor, manufacture date, and/or aggregate source. Using most scores, the flow number increases with an increase in *Vbe*, *Va*, VMA, VFA, and AC for the range studied in this study. The study by Kaloush [3] showed that the flow number decreases with an increase in air voids, which is contradictory to the results of the current study. This is due to the study range of air voids. The current study only investigated air void proportions between 3% and 6%.

3\* 3\* 3\* 3\* 3\* 3\* 3\* 3\* 3\* 3\* 

**Figure 5.** Groupwise average flow numbers.


**Table 5.** Summary of the effect of mix factors on the flow number of HMA.

#### **4. Conclusions**

This study evaluates the effects of mix factors such as VMA, void-filled with asphalt, effective binder content, etc. on the flow number of asphalt concrete. Laboratory testing was performed, and test results were analyzed using the statistical tools. The following conclusions can be made from this study:


6. The other five mixtures—S(100) PG 64-22, SX(75) PG 58-28, SX(75) PG 58-34, SX(75) PG 64-22, and SX(75) PG 64-28—had flow numbers less than 50; thus, they are considered good for traffic of less than 3 million ESALs.

Our recommendation for future research is that a flow number predictive model should be developed to determine the flow number of a new mix with more laboratory testing on a pre-planned test matrix.

**Author Contributions:** M.R.I. is the primary investigator of this research article. He is the lead researcher with collecting the research ideas, pursuing funding, execution, delivery and publication. S.A.K. supervised all aspects of this research including editing and proofreading. S.K.N. helped in data collection, analysis, and helped the team finally publish it.

**Funding:** This research is funded by the Colorado Department of Transportation (CDOT), Grant No. CDOT 417.01.

**Acknowledgments:** The Colorado State University—Pueblo (CSU-Pueblo) research team appreciates the research funding by the Colorado Department of Transportation (CDOT). It would like to express its sincere gratitude and appreciation to Jay Goldbaum, Michael Stanford, Aziz Khan, Melody Perkins, Keith Uren, Vincent Battista, Skip Outcalt, Bill Schiebel, and Roberto E. DeDios from the CDOT.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.
