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56 A Manual for Design of Hot Mix Asphalt with Commentary
calibrated
gage
vacuum
pump
vapor traps
vacuum container
Figure 5-8. Example of apparatus for vacuum
saturation of loose hot mix, part of the procedure
for determining maximum specific gravity of
asphalt concrete mixtures.
Volumetric Analysis
The previous sections give the reader the background needed to understand the primary
factors involved in volumetric analysis: mixture bulk and theoretical maximum specific gravity;
air void content; VMA; VFA; and effective binder content. This section describes the calcu-
lations involved in performing an actual volumetric analysis of asphalt concrete. It is similar
but not identical to the discussion of volumetrics given in the Asphalt Institute publications
Superpave Mix Design (SP-2) and Mix Design Methods (MS-2), both of which are good refer-
ences for technicians and engineers responsible for HMA mix design and analysis. This section
has been kept relatively short, since almost all laboratories currently have personal computers
that can be loaded with software for performing volumetric analysis. The Mix Design Tools
spreadsheet included with this manual includes software for performing volumetric analysis.
The basic equations are presented here as background for interested engineers and senior
technicians and for those interested in putting together their own spreadsheets for mix design
and analysis. Figure 5-9 illustrates the definitions of variables used to define various volumes as
used in volumetric analysis. The volume of permeable pores in the aggregate surface containing
asphalt shows up in three different terms: the aggregate bulk volume (Vsb), the total asphalt
volume (Vb), and the absorbed asphalt volume (Vba). Also, in this manual the convention
adopted for volume terms is that the capital letter V followed by a subscript denotes the absolute
volume of a particular component, whereas V followed by capital letters denotes a percent-
age by volume. Thus, Vma represents the absolute volume of voids in the mineral aggregate
(in units of cm3, for example), whereas VMA indicates the voids in the mineral aggregate as
a volume percentage.
A set of variables similar to those given in Figure 5-9 can be defined for the mass terms used
in volumetric analysis:
Mbe = Mass of effective asphalt binder
Mba = Mass of absorbed asphalt binder
Ms = Mass of aggregate, total
Mb = Mass of asphalt binder, total
Mse = Mass of aggregate, effective (excluding surface pores filled with asphalt)
Ma = Mass of air voids
Mmb = Mass of specimen, total

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Mixture Volumetric Composition 57
air Va
VMA
asphalt binder Vbe
Vb
absorbed
Vba
asphalt Vmb
Vmm
Vsb
aggregate Vse
Vbe = Volume of effective asphalt binder
VBE = Effective asphalt content, percent by volume
Vba = Volume of absorbed asphalt binder
VBA = Absorbed asphalt binder, percent by total mix volume
Vma = Volume of voids in mineral aggregate
VMA = Voids in mineral aggregate, percent by volume
Vsb = Volume of aggregate, bulk (including all permeable surface pores)
Vb = Volume of asphalt binder, total
VB = Total asphalt binder content, percent by volume
Vse = Volume of aggregate, effective (excluding surface pores filled with asphalt)
Va = Volume of air voids
VA = Air void content, volume percent
Vmm = Volume of aggregate and asphalt
Vmb = Volume of specimen, total
Figure 5-9. Definition of volume terms used in volumetric
analysis.
The set of variables for mass are slightly different than the ones for volume because the air
voids and the permeable pores in the aggregate surface have no mass. For the same reason, there
is no variable representing the mass of air voids or the mass of the asphalt binder plus air voids--
which would of course be the same as the mass of the binder alone.
In addition to these variables representing various volumes and masses, two additional variables
are used to represent percentages by weight [mass?] of asphalt binder and aggregate: Pb and Ps,
respectively. These are normally both percentages by mass [weight?] of the total mixture weight.
Equations
Average Aggregate Specific Gravity. Because the aggregate used in producing asphalt concrete
is almost always a blend of two or more aggregates, usually having different values for bulk
specific gravity, volumetric calculations such as the ones described below must be done using an
average bulk specific gravity for the aggregate blend. This average value can be calculated using
the following equation:
Ps1 A + Ps 2 A + Ps 3 A + . . .
Gsb = (5-3)
Ps1 A Ps 2 A Ps 3 A . . .
+ + +
Gsb1 Gsb 2 Gsb 3
where
Gsb = overall bulk specific gravity for aggregate blend
Ps1/A = volume % of aggregate 1 in aggregate blend
Gsb1 = bulk specific gravity for aggregate 1

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58 A Manual for Design of Hot Mix Asphalt with Commentary
Ps2/A = volume % of aggregate 2 in aggregate blend
Gsb2 = bulk specific gravity for aggregate 2
Ps3/A = volume % of aggregate 3 in aggregate blend
Gsb3 = bulk specific gravity for aggregate 3
Air Void Content. Air void content is calculated from the mixture bulk and theoretical
maximum specific gravity:
G
VA = 100 1 - mb (5-4)
Gmm
where
VA = Air void content, volume %
Gmb = Bulk specific gravity of compacted mixture
Gmm = Theoretical maximum specific gravity of loose mixture
Asphalt Binder Content. Asphalt binder content can be calculated in four different ways:
total binder content by weight, effective binder content by weight, total binder content by
volume, and effective binder content by volume. Total asphalt content by volume is calculated
as the percentage of binder by total mix mass:
Mb
Pb = 100
M s + Mb
(5-5)
where
Pb = Total asphalt binder content, % by mix mass
Mb = Mass of binder in specimen
Ms = Mass of aggregate in specimen
Total asphalt binder content by volume can be calculated as a percentage of total mix volume
using the following formula:
PbGmb
VB = (5-6)
Gb
where
VB = Total asphalt binder content, % by total mix volume
Pb = Total asphalt binder content, % by mix mass
Gmb = Bulk specific gravity of the mixture
Gb = Specific gravity of the asphalt binder
The absorbed asphalt binder content by volume is also calculated as a percentage of total mix
volume:
P P 100
VBA = Gmb b + s - (5-7)
Gb Gsb Gmm
where
VBA = Absorbed asphalt content, % by total mixture volume
Gmb = Bulk specific gravity of the mixture

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Mixture Volumetric Composition 59
Pb = Total asphalt binder content, % by mix mass
Gb = Specific gravity of the asphalt binder
Ps = Total aggregate content, % by mix mass
= 100 - Pb
Gsb = Average bulk specific gravity for the aggregate blend
Gmm = Maximum specific gravity of the mixture
The effective asphalt by volume is found by subtracting the absorbed asphalt content from the
total asphalt content:
VBE = VB - VBA (5-8)
where
VBE = Effective asphalt content, % by total mixture volume
VB = Total asphalt binder content, % by mixture volume
VBA = Absorbed asphalt content, % by total mixture volume
The effective and absorbed asphalt binder contents can also be calculated as percentages by
weight, once the volume percentage has been calculated:
VBE
Pbe = Pb
VB
(5-9)
Pba = Pb - Pbe (5-10)
where
Pbe = Effective asphalt binder content, % by total mass
Pb = Asphalt binder content, % by total mass (see Equation 5-5)
VBE = Effective asphalt binder content, % by total mixture volume (see Equation 5-8)
VB = Asphalt binder content, % by total mixture volume (see Equation 5-6)
Pba = Absorbed asphalt binder, % by total mixture mass
VMA is simply the sum of the air void content and the effective asphalt binder content by
volume:
VMA = VA + VBE (5-11)
where
VMA = Voids in the mineral aggregate, % by total mixture volume
VA = Air void content, % by total mixture volume (Equation 5-4)
VBE = Effective binder content, % by total mixture volume (Equation 5-8)
VFA is the effective binder content expressed as a percentage of the VMA:
VBE
VFA = 100
VMA
(5-12)
where VFA is the voids filled with asphalt, as a volume percentage.

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60 A Manual for Design of Hot Mix Asphalt with Commentary
Apparent Film Thickness. Apparent film thickness can be calculated using the following
formula:
1, 000VBE
AFT = (5-13)
Ss PsGmb
where
AFT = Apparent film thickness, µm
VBE = Effective binder content, % by total mix volume (see Equation 5-8)
Ss = Aggregate specific surface, m3/kg
Ps = Aggregate content, % by total mix weight
= 100 - Pb
Gmb = Mixture bulk specific gravity
Aggregate Specific Surface. The surface area of aggregate contained in a mixture, expressed
as specific surface, is needed to calculate apparent film thickness. Specific surface values used in
asphalt concrete mix design and analysis are not true specific surface values--they are effective
specific surface values, in which some portion of the finest mineral dust is eliminated from the
calculation. Unfortunately, aggregate specific surface as it applies to mix design technology cannot
be precisely defined; traditional, highly empirical methods for calculating aggregate specific surface
became thoroughly embedded in mix design practice, but were largely based on engineering
judgment and experience and were never well documented. The methods presented here are
taken from NCHRP Report 567 and have been devised to provide values consistent with traditional
aggregate specific surface values. A very easy and accurate method to estimate aggregate specific
surface is to add the % passing the 0.30-, 0.15- and 0.075-mm sieves and divide by 5:
P0.30 + P0.15 + P0.075
Ss (5-14)
5
where
Ss = Aggregate specific surface, m2/kg
P0.30 = % of aggregate passing 0.30-mm sieve
P0.15 = % of aggregate passing 0.15-mm sieve
P0.075 = % of aggregate passing 0.075-mm sieve
A more rigorous calculation requires calculation of the contribution of each size fraction to
the total specific surface of the aggregate:
1.4 ( P50 - P37.5 ) + 2.0 ( P37.5 - P25 ) + 2.8 ( P25 - P19.5 ) + 3.9 ( P19.5 - P12.5 )
1 + 5.5 ( P12.5 - P9.5 ) + 8.9 ( P9.5 - P4.75 ) + 17.9 ( P4.75 - P2.36 )
Ss = (5-15)
1, 000Gsb + 36.0 ( P2.36 - P1.18 ) + 71.3( P1.18 - P0.60 ) + 141( P0.60 - P0.30 )
+ 283( P0.30 - P0.15 ) + 566 ( P0.15 - P0.075 ) + 1, 600 ( P0.075 )
In Equation 5-15, the Ps represent percent passing for the sieve size in mm represented by the
subscript for each P. The calculation appears complicated, but simply involves multiplying the
percent of material between each successive pair of sieves by a factor (1.4, 2.0, 2.8, etc.), sum-
ming the results, and then dividing by 1,000 times the aggregate bulk specific gravity. Equa-
tion 5-15 is quite tedious, but can be entered into a spreadsheet for use in routine calculations.
However, given the empirical nature of aggregate specific surface area, it is not clear that there is
any advantage in using Equation 5-15 compared to the much simpler Equation 5-14.

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Mixture Volumetric Composition 61
Example Problem 5-1. Volumetric Analysis of an HMA Mixture
An example problem in mixture volumetric analysis is given below. The data
needed for the problem is first presented in Tables 5-1 through 5-3. Then, the
calculations are shown in the typical order in which they would be performed.
A table summarizing the results of the analysis is presented at the end of the
example.
Table 5-1. Mixture composition for
example problem.
Percent by Mass Percent by
Specific in Aggregate Mass in
Material Gravity Blend Total Mix
12.5-mm limestone 2.621 28.0 26.6
12.5-mm sandstone 2.668 28.0 26.6
Manufactured sand 2.595 44.0 41.8
Asphalt binder 1.030 --- 4.9
Table 5-2. Gradation
data for example
problem.
%
Sieve Size Passing
19 mm 100
12.5 mm 92
9.5 mm 82
4.75 mm 55
2.36 mm 32
1.18 mm 24
0.600 mm 18
0.300 mm 11
0.150 mm 9
0.075 mm 5.5
Table 5-3. Mixture bulk and maximum specific
gravity data for example problem.
Measurement Mass, g
Bulk Specific Gravity
Dry weight in air 4,299.3
Saturated surface-dry weight in air 4,333.7
Weight in water 2,510.0
Maximum Specific Gravity
Dry weight in air 4,295.0
Weight of container filled with water 7,823.1
Weight of container with specimen filled with water 10,365.5
(continued on next page)

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62 A Manual for Design of Hot Mix Asphalt with Commentary
Example Problem 5-1. (Continued)
Solution
Step 1. Determine the aggregate average bulk specific gravity using Equation 5-3:
28 + 28 + 44
Gsb = = 2.622
28 28 44
+ +
2.621 2.668 2.595
Step 2. Determine the mixture bulk specific gravity using Equation 5-1:
4, 299.3
Gmb = = 2.357
4, 333.7 - 2,510.0
Step 3. Determine the mixture maximum specific gravity using Equation 5-2:
4, 295.0
Gmm = = 2.451
4, 295.0 + 7, 823.1 - 10, 365.5
Step 4. Calculate the air void content using Equation 5-4:
2.357
VA = 100 1 - = 3.8%
2.451
Step 5. Calculate the total asphalt binder content by mix volume using
Equation 5-6:
4.9 × 2.357
VB = = 11.2%
1.03
Step 6. Calculate the absorbed asphalt binder content by mix volume using
Equation 5-7:
4.9 95.1 100
VBA = 2.357 + - = 0.5%
1.03 2.622 2.451
Step 7. Calculate the effective asphalt binder content by volume by subtracting
the absorbed asphalt from the total asphalt content (Equation 5-8):
VBE = 11.2 - 0.5 = 10.7%
Step 8. Calculate the effective and absorbed asphalt contents by total mix weight
using Equations 5-9 and 5-10:
10.7
Pbe = 4.9 = 4.7%
11.2
Pba = 4.9 - 4.7 = 0.2%

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Mixture Volumetric Composition 63
Example Problem 5-1. (Continued)
Step 9. Calculate the VMA by adding the air void content and the effective asphalt
binder content by volume (Equation 5-11):
VMA = 3.8 + 10.7 = 14.5%
Step 10. Calculate the VFA using Equation 5-12:
10.7
VFA = 100 = 73.8%
14.5
Step 11. Estimate the specific surface of aggregate using Equation 5-14:
11 + 9 + 5.5
Ss = 5.1 m2 kg
5
Step 12. Calculate the apparent film thickness using Equation 5-13:
1, 000 × 10.7
AFT = = 9.4 m
5.1 × 95.1 × 2.357
Table 5-4 summarizes the results of the volumetric analysis example problem.
Table 5-4. Summary of volumetric analysis
example problem.
Mixture Composition Factor Value
Total asphalt binder content, % by mix weight 4.9
Absorbed asphalt binder, % by mix weight 0.5
Aggregate content, % by mix weight 95.1
Average aggregate bulk specific gravity 2.622
Mixture bulk specific gravity 2.357
Mixture maximum specific gravity 2.451
Air void content, % by total mix volume 3.8
Effective asphalt binder content, % by total mix volume 10.7
VMA, % by total mix volume 14.5
VFA, % by total mix volume 73.8
Aggregate specific surface, m2/kg 5.1
Apparent film thickness, m 9.4
Requirements for Asphalt Concrete Composition
Specific values for volumetric mix factors for different mix types are not presented here.
Instead, they are given in the chapter covering the design of each type of material: Chapter 8,
dense-graded HMA mixtures; Chapter 10, gap-graded HMA, and Chapter 11, open-graded
friction course mixtures.
Bibliography
AASHTO Standards
R 35, Superpave Volumetric Design for Hot-Mix Asphalt (HMA)
T 166, Bulk Specific Gravity of Compacted Asphalt Mixtures Using Saturated Surface-Dry Specimens

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64 A Manual for Design of Hot Mix Asphalt with Commentary
T 209, Theoretical Maximum Specific Gravity and Density of Bituminous Paving Mixtures
T 269, Percent Air Voids in Compacted Dense and Open Asphalt Mixtures
T 275, Bulk Specific Gravity of Compacted Bituminous Mixtures Using Paraffin-Coated Specimens
Other Publications
The Asphalt Institute (1997) Mix Design Methods for Asphalt Concrete and Other Hot-Mix Types (MS-2), 6th Ed.,
141 pp.
The Asphalt Institute (2001) Superpave Mix Design (SP-2), 128 pp.
Christensen, D. W., and R. F. Bonaquist (2006) NCHRP Report 567: Volumetric Requirements for Superpave Mix
Design, Final Report for NCHRP Projects 9-25 and 9-31, TRB, National Research Council, Washington, DC,
57 pp.
Prowell, B. D. and E. R. Brown (2007) NCHRP Report 573: Superpave Mix Design: Verifying Gyration Levels in
the Ndesign Table, TRB, National Research Council, Washington, DC, 73 pp.