# The Delta Tc Parameter: What Is It and How Do We Use It?

You may have heard of a new asphalt binder parameter being discussed recently for evaluating age related cracking potential. ΔTc (pronounced delta tea see) is defined as the numerical difference between the low continuous grade temperature determined from the Bending Beam Rheometer (BBR) stiffness criteria (the temperature where stiffness, S, equals 300 MPa) and the low continuous grade temperature determined from the BBR m-value (the temperature where m equals 0.300). If you aren’t sure how to determine low temperature continuous grades, you can find instructions in ASTM D7643, Standard Practice for Determining the Continuous Grading Temperature and Continuous Grades for PG Graded Asphalt Binders. Don’t forget to subtract 10°C from your BBR test temperatures when determining low temperature continuous grades!

For example, let’s say a set of BBR tests yielded the following results at two test temperatures:

-18°C : Stiffness = 243 MPa and m-value = 0.309

-24°C : Stiffness = 400 MPa and m-value = 0.256

Using these results, the low continuous grade temperature for the stiffness criteria (Tcont, S) equals -30.5°C and the low continuous grade temperature for the m-value criteria (Tcont, m) equals -29.0°C. Once you have the temperatures, just subtract Tcont, m from Tcont, S to get the value of ΔTc.

For this example: ΔTc = -30.5 - (-29.0) = -1.5.

It’s that simple! The ΔTc parameter can be measured on any asphalt binder, whether it’s a virgin asphalt binder or binder that’s been extracted and recovered from a sample of asphalt mixture.

Now that you know what ΔTc is and how it’s calculated, let’s discuss how it relates to asphalt pavement performance and what it shows us that we can’t get from BBR stiffness and m-value results alone. ΔTc was first proposed by Asphalt Institute engineer Mike Anderson in 2011 to measure the ductility loss of aged asphalt binder as part of a study examining relationships between asphalt binder properties and non-load related cracking. In particular, the study focused on finding a parameter to explain block cracking in airport pavements.

Block cracking is a non-load related cracking phenomenon similar to thermal cracking that causes cracks to develop in both longitudinal and transverse directions. This results in a square or “block” pattern. Block cracking is most often seen in significantly aged pavements with low traffic volumes. The lack of traffic allows the asphalt binder to develop a type of internal structure (thixotropic hardening) that will exhibit brittle behavior when exposed to thermal stresses. Although it’s similar to thermal cracking, studies have shown that block cracking may be more dependent on the age of the asphalt pavement than on the environmental conditions. In other words, an older pavement that does not experience environmental conditions that would cause thermal cracking may still experience block cracking.

Figure 1: Block Cracking on the NCAT Test Track

Ductility is defined as the ability of a material to be stretched without breaking. This is important in flexible pavements because the thin films of asphalt binder between the aggregate particles must have a certain amount of ductility to withstand stresses in the pavement due to traffic or temperature changes. Prior to the Superpave Performance Grading (PG) system, ductility was used as a surrogate relaxation parameter for asphalt binders and was considered a way to distinguish cracking performance. In general, research has shown that ductility may be an important factor in cracking performance as asphalt pavements age. In particular, pavements with low ductility binders tend to exhibit poor cracking performance, even when the overall asphalt binder stiffness values is similar to that of pavements that perform well. These observations imply that asphalt binder stiffness and relaxation may not change at the same rate due to aging and that the loss in relaxation (or ductility) may have a more significant effect on cracking performance than the increase in stiffness.

Our current Superpave PG system does not include a direct measure of ductility. Instead, it relies on relaxation parameters such as the phase angle measured by the Dynamic Shear Rheometer (DSR) at intermediate temperatures and the BBR m-value at low temperatures to predict cracking performance. While these parameters are suitable for determining the relaxation properties needed for other types of cracking, they do not provide a relationship between stiffness and ductility that may be needed to control block cracking.

Other studies have shown that as some asphalt binders age, their low temperature relaxation properties, as measured by the BBR m-value, deteriorate significantly faster than their low temperature stiffness increases. This leads us back to the possible use of ΔTc. The next version of AASHTO PP78 Design Considerations When Using Reclaimed Asphalt Shingles (RAS) in Asphalt Mixtures, to be released later this year, includes a criteria for ΔTc as part of the mix design process. Extracted and recovered binders from mixtures containing RAS are to be aged in a pressure aging vessel (PAV) for 40 hours before BBR testing and determining ΔTc. The minimum ΔTc criteria is -5.0°C, meaning that a recovered and aged binder with a ΔTc of -6.0°C is not acceptable. The revised PP 78 contains notes that allow the ΔTc criteria to be adjusted based on local experience or the use of a mixture cracking test implemented by the agency in lieu of the criteria for ΔTc.

In summary, the ΔTc parameter has been proposed as a relatively simple method for measuring the loss of relaxation properties of asphalt binders. Although data on this parameter as an indicator of binder brittleness continues to be collected, some agencies may begin to use it as a criteria for RAS mixes and are considering expanding its use to evaluate the impact of REOB and the effectiveness of rejuvenators and soft asphalts with mixtures containing RAP.