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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.