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Publication Number: FHWA-HRT-10-035
Date: September 2011


LTPP Computed Parameter: Dynamic Modulus



Until the advent of the Superpave™ mix design system in the early 1990s, the viscosity of asphalt binders was the key measure used in purchase specifications. As a result, many sections that are now reaching their design lives and, as a result, are included in the LTPP database, contain various measures of viscosity. Over the years, four primary types of viscosity measures have been adopted: (1) ring and ball temperature (R&BT), (2) penetration (at various temperatures), (3) absolute viscosity at 140 °F (60 °C), and (4) kinematic viscosity at 275 °F (135 °C). These measures have been used together or separately in various grading schemes. With the exception of penetration, these viscosity measures are beyond the range of temperature conditions typically needed for modulus prediction. As a result, a certain amount of processing the available data is necessary. In this appendix, the steps necessary to properly analyze available viscosity data are presented.


Although the relationship between viscosity and temperature is highly nonlinear, it has been found that when proper transformations are made to temperature and viscosity, a linear relationship exists. This relationship is commonly referred to as the “A-VTS relationship.”(43) This relationship is shown schematically in figure 79 and mathematically in equation 56. The plateau region in figure 79 is based on arguments that are, in turn, based on the chemical structure of asphalt binder and suggest that the maximum viscosity for asphalt binder is 2.7 x 1012 cP (0.0027 x 1012 Pas).(44) For the purposes of this report, this same limiting criterion was also adopted.

Figure 79. Graph. A–VTS relationship. This figure shows a linear relationship between the logarithm base 10 of the logarithm base 10 of the viscosity and the logarithm of temperature when expressed in Rankine for measured viscosity database and regression intercept–regression slope of viscosity temperature susceptibility (A–VTS) relationship. The logarithm of the logarithm of viscosity is shown on the y–axis in centipoise from 0 to 1.2 cP, and the logarithm base 10 of temperature in Rankine, TR, is shown on the x–axis from 2.55 to 2.9. The logarithm of the logarithm of viscosity is shown to increase with the decrease in the logarithm of temperature until a critical value is reached. The critical viscosity value is equal to 2.7 × 1012 cP and is represented by a solid horizontal line.
Figure 79. Graph. A-VTS relationship.

Equation 56. Calculation of viscosity. The logarithmic base 10 of logarithmic base 10 of parenthesis eta end parenthesis equals parenthesis A plus the product of VTS times the logarithmic base 10 of parenthesis T subscript R end parenthesis for T subscript R greater than T subscript critical. The logarithmic base 10 of logarithmic base 10 of parenthesis eta end parenthesis equals 2.7 times 10 superscript 12 for T subscript R less than or equal to T subscript critical. (56)


η = Viscosity (cP).
A = Intercept of temperature susceptibility relationship.
VTS = Slope of temperature susceptibility relationship.
TR = Temperature in Rankine.
Tcritical = Temperature in Rankine at which the viscosity is equal to 2.7 x 1012 cP (0.0027 x 1012 Pas).

Because the A-VTS relationship is linear, only two of the four viscosity measures are needed to completely characterize the relationship. The following sections provide the equations necessary to convert the four measures to actual viscosity.


The softening point of asphalt binder as measured by AASHTO T53-08 is also known as R&BT.(45) According to literature on the topic, this temperature, measured in Fahrenheit, corresponds to the temperature at which asphalt binder has a viscosity of 13,000 P (1,300 Pas).(44)


The penetration number for asphalt binder is determined via AASHTO T49-07.(46) In this test, a 3.5-oz (100-g) needle is used to penetrate an asphalt sample for 5 s. The amount of penetration, measured in tenths of a millimeter, is the penetration number for the asphalt binder at the particular test temperature. The measurement temperature typically used for specification purposes is 77 °F (25 °C); however, other temperatures, including 39.2 and 115 °F (4 and 46 °C), may also be measured. Penetration values are converted to viscosity using the relationship suggested by Mirza and Witczak as seen in equation 57:(44)

Equation 57. Mirza and Witczak relationship to calculate the viscosity. The logarithmic base 10 of eta equals to 10.5012 minus 2.26011 times logarithmic base 10 of parenthesis PEN end parenthesis plus the product of 0.00389 times parenthesis logarithmic base 10 of parenthesis PEN end parenthesis, end parenthesis squared. (57)


η = Viscosity (P).
PEN = Penetration number at a given test temperature.


The absolute viscosity is the viscosity of asphalt binder measured at 140 °F (60 °C) by AASHTO T202-03.(47) Because this quantity is typically reported in poise instead of centipoise, the only conversion needed is to multiply the given quantity by 100.


The kinematic viscosity of asphalt binder is determined at 275 °F (135 °C) via AASHTO T201-03.(48) Kinematic and absolute viscosities are related by the density of the medium under investigation. The relationship between these two quantities is shown in equation 58. For LTPP purposes, it is assumed that the density for all binders is equal to 0.6 oz/in3 (1.03 g/cm3).

Equation 58. Calculation of absolute viscosity. Eta equals nu times rho. (58)


η = Absolute viscosity (cP).
ν = Kinematic viscosity (cSt).
ρ = Density (oz/in3 ((g/cm3)).


For a given asphalt binder, the following properties are measured:

R&BT temperature = 104 °F (40 °C)
PEN at 39.2 °F (4 °C) = 19
PEN at 77.0 °F (25 °C) = 156
η = 774 P (77.4 Pas)
ν = 266.1 centistokes (cSt)

Using these relationships, the viscosity is computed for different temperatures as follows:

39.2 °F (4 °C) = 4.14 × 109 cP (0.00414 × 109 Pas)
77.0 °F (25 °C) = 3.66 × 107 cP (0.00366 × 107 Pas)
104 °F (40 °C) = 1.30 × 106 cP (0.0013 × 106 Pas)
140 °F (60 °C) = 7.74 × 105 cP (0.00774 × 105 Pas)
275 °F (135 °C) = 2.74 × 102 cP (0.00274 × 102 Pas)

After performing linear regression on these quantities, it is found that A = 10.599, VTS = -3.5646, and Tcritical = 464.8 °R.


As part of the NCHRP 1-37A effort, researchers compiled typical A and VTS values for different purchase specification grades.(2) These typical values include Superpave™ PG binders, AC viscosity-graded binders, and penetration-graded binders. Data were not compiled for all grades in use across the United States, but most grades were included. Because some of the LTPP layers fell in the category where the only binder information known was the grade, these relationships are considered important. In table 36, the A and VTS parameters are presented for the different grades reported in the MEPDG documentation.(2)

Table 36. Relationship between asphalt binder grade and viscosity parameters.
Asphalt Binder Grade A VTS Asphalt Binder Grade A VTS
PG 46-34 11.5040 −3.9010 PG 70-28 9.7150 −3.2170
PG 46-40 10.1010 −3.3930 PG 70-34 8.9650 −2.9480
PG 46-46 8.7550 −2.9050 PG 70-40 8.1290 −2.6480
PG 52-10 13.3860 −4.5700 PG 76-10 10.0590 −3.3310
PG 52-16 13.3050 −4.5410 PG 76-16 10.0150 −3.3150
PG 52-22 12.7550 −4.3420 PG 76-22 9.7150 −3.2080
PG 52-28 11.8400 −4.0120 PG 76-28 9.2000 −3.0240
PG 52-34 10.7070 −3.6020 PG 76-34 8.5320 −2.7850
PG 52-40 9.4960 −3.1640 PG 82-10 9.5140 −3.1280
PG 52-46 8.3100 −2.7360 PG 82-16 9.4750 −3.1140
PG 58-10 12.3160 −4.1720 PG 82-22 9.2090 −3.0190
PG 58-16 12.2480 −4.1470 PG 82-28 8.7500 −2.8560
PG 58-22 11.7870 −3.9810 PG 82-34 8.1510 −2.6420
PG 58-28 11.0100 −3.7010 AC-2.5 11.5167 −3.8900
PG 58-34 10.0350 −3.3500 AC-5 11.2614 −3.7914
PG 58-40 8.9760 −2.9680 AC-10 11.0134 −3.6954
PG 64-10 11.4320 −3.8420 AC-20 10.7709 −3.6017
PG 64-16 11.3750 −3.8220 AC-3 10.6316 −3.5480
PG 64-22 10.9800 −3.6800 AC-40 10.5338 −3.5104
PG 64-28 10.3120 −3.4400 PEN 40-50 10.5254 −3.5047
PG 64-34 9.4610 −3.1340 PEN 60-70 10.6508 −3.5537
PG 64-40 8.5240 −2.7980 PEN 85-100 11.8232 −3.6210
PG 70-10 10.6900 −3.5660 PEN 120-150 11.0897 -3.7252
PG 70-16 10.6410 −3.5480 PEN 200-300 11.8107 −4.0068
PG 70-22 10.2990 -3.4260

— Indicate that no additional relationships exist.



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The Federal Highway Administration (FHWA) is a part of the U.S. Department of Transportation and is headquartered in Washington, D.C., with field offices across the United States. is a major agency of the U.S. Department of Transportation (DOT). Provide leadership and technology for the delivery of long life pavements that meet our customers needs and are safe, cost effective, and can be effectively maintained. Federal Highway Administration's (FHWA) R&T Web site portal, which provides access to or information about the Agency’s R&T program, projects, partnerships, publications, and results.
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