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46 Understanding the terminology used to describe the volumetric composition of asphalt concrete and the ability to perform a volumetric analysis are two of the most important skills that engineers and technicians must master in order to develop effective asphalt concrete mix designs. Most of the specifications for HMA and related materials used throughout the United States and Canada are expressed, at least in part, in terms of volumetric composition. This chapter describes the basic terminology used in volumetric analysis, including such important concepts as air void content, voids in the mineral aggregate, and apparent film thickness. Besides basic definitions of such terms, an effort has been made to briefly describe how each of the main mix composition factors affect pavement performance. Because accurate bulk and maximum theoretical specific gravity data are essential to performing volumetric analysis, these tests are described in some detail in this chapter. Equations are presented for performing a complete volumetric analysis, and a detailed example problem is given at the end of the chapter. Because most engineers and technicians use spreadsheets and similar tools to perform the calculations involved in volumetric analysis of HMA mixtures, detailed reading of the equations and example problems will not be necessary for many readers of this manual; however, the equations and example problem are presented to (1) make the chapter complete and (2) for engineers and advanced technicians who wish to have a thorough understanding of volumetric analysis or who are interested in developing their own customized spreadsheets for performing volumetric analysis. Composition Factors Asphalt concrete primarily consists of three different components or phases: aggregate, asphalt binder, and air. Materials like concrete, which consist of particles held together by a cement of any type, are called composites. Some asphalt concrete mixtures contain small amounts of other additives, such as cellulose fibers, mineral fibers, ground rubber, and polymers. Although such additives may affect workability and performance significantly, these additives almost always represent a very small percentage of the overall volume and mass of the asphalt concrete. Engineers and technicians should remember the three major components of asphalt concreteâaggregate, asphalt, and air. These three components are the key to understanding volumetric analysis. The composition of asphalt concrete can be described in terms of either weight or volume. The asphalt binder content of a mixture, for example, is often given in terms of percent of total mix weight, whereas air void content is always given as a percent of total volumeâit must be given this way, since the mass of air voids in an asphalt concrete specimen is essentially zero. Although composition of asphalt concrete mixtures can be given in terms of weight, traditionally the most common and most important method of describing and analyzing asphalt concrete composition is by volume. This is what is meant by the term âvolumetricsâ or âvolumetric analysisâ of asphalt concreteâcharacterizing the composition of an asphalt concrete mixture by relative proportions C H A P T E R 5 Mixture Volumetric Composition
by volume of aggregate, asphalt, and air voids. Although this may sound like a simple task, it can become quite complicated when absorption of asphalt by the aggregate must be accounted for or when only incomplete information on a mixture is available. It is essential that engineers and technicians responsible for developing asphalt concrete mix designs or performing quality control operations have a thorough understanding of volumetric analysis. Typical asphalt concrete mixtures, as designed in the laboratory, contain about 84 to 90% aggregate, 6 to 12% asphalt binder, and about 4% air voids by volume. Figure 5-1 illustrates the typical composition of three different types of HMAâin all cases, almost all of the mixture volume is made up of aggregate. Asphalt concrete is mostly composed of aggregate. If the volume percentage of two of these components is known, the other can be determined by subtraction. For example, if we know that a mixture is to be designed with 4% air voids and 10% asphalt binder by volume, we can calculate the amount of aggregate required as 100 â (4 + 10) = 86% by volume. It is important to remember this when specifying the composition of asphalt concrete. It would be impossible, in this example, to specify a mixture with 4% air voids, 10% minimum binder content and 87% minimum aggregate content by volumeâa mixture with a minimum of 87% aggregate by volume could have no more that 13% total volume of air voids and asphalt binder. This is only one example of the complex interrelationships involved in characterizing and specifying the volumetric composition of asphalt concrete. More examples are given throughout this chapter. But first, we will discuss in more detail different volumetric factors used in volumetric analysis. Air Voids âAir voids,â when applied to asphalt concrete, means small pockets of air that exist within the asphalt binder and between aggregate particles. Air void content does not include pockets of air within individual aggregate particles, or air contained in microscopic surface voids or capillaries on the surface of the aggregate. Figure 5-2 shows the different ways in which air exists in asphalt concrete mixtures. Designing and maintaining the proper air void content in HMA and other mix types is important for several reasons. When air void contents are too high, the pavement may be too permeable to air and water, resulting in significant moisture damage and rapid age hardening. When air void contents are too low, the asphalt binder content may be too high, resulting in a mixture prone to rutting and shoving. When discussing the air void content of asphalt concrete mixtures, it is first necessary to specify what type of specimen or sample we are testing or analyzing. We can measure the air void content of asphalt concrete in the following types of specimens: â¢ Specimens compacted in the laboratory when developing a mix design â¢ Specimens compacted in the laboratory from material produced at the plant as part of quality assurance testing Mixture Volumetric Composition 47 0% 20% 40% 60% 80% 100% Lean Base Course Surface Course Stone Matrix Asphalt Voids Asphalt Aggregate Figure 5-1. Typical composition by volume of different HMA mix types.
â¢ Specimens taken from the roadway as cores immediately after construction as part of quality assurance testing â¢ Specimens taken from a wheel path of a roadway as cores after several years or more of traffic loading â¢ Specimens taken from between the wheel paths of a roadway as cores after several years or more of traffic loading The typical air void content of these different types of specimens will usually vary substantially, so it is important when discussing or specifying the air void content of asphalt concrete to make sure it is clear what type of specimen has been tested or is required to be tested. In the Superpave method of designing HMA, the air void content in laboratory mix designs is held constant at 4.0%. Some agencies have, however, expanded the allowable range for air void content to as wide as 3.0 to 5.0%, which was the design range used in the Marshall mix design method. The in-place air void content of HMA pavement is often assumed to be about 7%, but recent research (as reported in NCHRP Report 573) suggests that immediately after construction the air void content of HMA pavements typically ranges from about 6 to 11%, with a median value between 8 and 9%. Cores taken from a newly constructed pavement will generally have air void contents in this range. However, once the pavement is opened to traffic, the repeated loading as trucks pass over the pavement will tend to further compact the material in the wheel paths of the pavement. Many engineers assume that the air void content in the wheel paths of an asphalt concrete pavement should, within a few years, reach about the same value as was used in the laboratory mix design, but, as documented in NCHRP Report 573, this is not always the case. Cores taken outside the wheel path will undergo little or no change in air void content with time, since their location is not subjected to traffic loading. Therefore, if there is a question about how well an asphalt concrete pavement has been constructed several years after construction, this can only be determined from cores taken from between the wheel paths. Samples of HMA loose mix produced at the plant and compacted in the laboratory (commonly termed plant-produced/ laboratory-compacted) should have air void contents close to the design value. However, plant- produced HMA often contains more mineral dust than was used in the mix design, which tends to reduce the air void content of laboratory-compacted specimens. This reduction can be avoided by making sure that aggregate gradations used in preparing mix designs accurately reflect what is typically produced at the plant. 48 A Manual for Design of Hot Mix Asphalt with Commentary Air voids Pores on aggregate surface Air pockets within aggregate particle Asphalt Binder Figure 5-2. Air in asphalt concrete. Air can exist in pores on the aggregate surface, pockets within aggregate particles, or voids within the asphalt binder or between the binder and aggregate particles. Only the last type of air is included in the air void content of asphalt concrete mixtures.
Determining air void content is one of the main purposes of volumetric analysis. Unfortunately, there is no simple direct way to determine the air void content of an asphalt concrete specimen. Air void content is determined by comparing the specific gravity (or density) of a compacted specimen with the maximum theoretical density of the mixture used to make that specimen. For example, if the compacted density of an asphalt concrete specimen is 95.3% of the theoretical maximum specific gravity, the air void content is 100 â 95.3 = 4.7%. Mixture-specific gravity and the volumetric analysis of asphalt concrete are discussed in more detail later in this chapter. Binder Content Binder content is one of the most important characteristics of asphalt concrete. Use of the proper amount of binder is essential to good performance in asphalt concrete mixtures. Too little binder will result in a dry stiff mix that is difficult to place and compact and will be prone to fatigue cracking and other durability problems. Too much binder will be uneconomical, since asphalt binder is, by far, the most expensive component of the mixture and will make the mixture prone to rutting and shoving. Typical asphalt binder contents range from 3.0% or less (for lean base course mixtures) to over 6.0% (for surface course mixtures and rich bottom layers), which are designed for exceptional durability and fatigue resistance. As mentioned earlier in this chapter, asphalt binder content is most often stated and specified as a percentage of total mix weight. A ton of hot mix that is 5.2% asphalt binder will contain 2,000 Ã 0.052 = 104 pounds of binder. However, there are two problems with this way of stating asphalt content. First and most important, it is the asphalt content by volume and not by weight that dictates performance, and asphalt content by total mix weight is a function of both asphalt content by volume and aggregate specific gravity. Consider two asphalt concrete mixtures, both with an air void content of 4.0% and an asphalt binder content of 12.0% by volume. One mixture is made with a limestone aggregate with a specific gravity of 2.50, and the other with a dense diabase having a specific gravity of 3.20. If no asphalt binder is absorbed by the aggregate (as we will discuss below, not a very good assumption), the asphalt content of the limestone mix will be 5.35% by total mix weight, while the asphalt content of the diabase mixture will be 4.23% by total mix weight. The difference in asphalt binder content by weight is over 1.0%, even though these mixtures contain identical asphalt contents by volume! To avoid this problem, many agencies now specify minimum binder content by weight as a function of aggregate specific gravity. The second problem with stating asphalt binder content by total mix weight is that most aggregates tend to absorb asphalt binder. Asphalt binder absorbed by an aggregate is tightly held in microscopic pores on the aggregate surface and does not significantly contribute to the durability of a mixture. The amount of absorption varies widely, depending on aggregate type. Dense igneous rocks, such as diabase and basalt, might only absorb a few tenths of a percent of asphalt binder from a mixture, while porous sandstones and slags might absorb from 1 to as much as 4% of the asphalt binder from a mixture. The term âeffective binder content,â abbreviated as Vbe, is used to describe the amount of asphalt binder in a mixture not including that absorbed by the aggregate (see Figure 5-3). For example, if the total asphalt content of a mixture is 5.3% by weight, and the aggregate absorbs 0.4% binder by total mix weight, the effective binder content of this mixture is 5.3 â 0.4 = 4.9%. If a mixture is to be designed to have 11.0% asphalt content by volume, not including the 1.0% of the binder absorbed by the aggregate, then the total asphalt binder content must be 11.0 + 1.0 = 12.0% by volume. Theoretically, the most effective way of characterizing and specifying asphalt binder content is effective binder content by volume, since this avoids the two problems described above. However, effective asphalt content by volume can only be determined through volumetric analysis and cannot be determined with a high degree of precision. Asphalt concrete plants are almost always designed to control asphalt binder content as a percentage of total mix weight. For these reasons, Mixture Volumetric Composition 49
many agencies specify minimum total binder content by weight and give tables, graphs, or formulas adjusting this minimum according to the aggregate specific gravity. Unfortunately, there is no simple way to account for aggregate absorption when specifying asphalt binder content, since absorption varies so widely among aggregate types, and even substantially within aggregate from a given quarry. As discussed below, one way to specify effective binder content by volume is to control both air void content and voids in the mineral aggregate at the same time. Voids in the Mineral Aggregate Voids in the mineral aggregate (VMA) refers to the space between aggregate particles in an asphalt concrete mixture (see Figure 5-4). VMA is also often used to characterize loose aggregate, 50 A Manual for Design of Hot Mix Asphalt with Commentary Figure 5-3. Effective asphalt content. Effective asphalt includes asphalt binder not absorbed by the aggregateâ in this sketch, the cross-hatched gray area represents effective binder. Figure 5-4. Voids in mineral aggregate. Dark and light gray areas represent aggregate particles, black area asphalt binder and white areas air voids; voids in mineral aggregate (VMA) is composed of asphalt binder and air voidsâblack and white areas.
but its meaning is exactly the sameâthe volume percentage of space between aggregate particles. VMA is numerically equal to the air void content plus the effective binder content by volume. Therefore, establishing a single design air void content (such as the 4.0% used in Superpave mixtures) and then controlling VMA is the same as controlling effective binder content. For example, a Superpave 12.5-mm mixture designed at 4.0% air voids with 14.0% minimum VMA has a minimum effective binder content of 14.0 â 4.0 = 10.0% by volume. Some engineers and agencies have proposed that VMA should be defined as total binder content plus air void content, both by volume. The only advantage to using this definition is that it makes aggregates with high absorption appear to be more economical than they are, since defining VMA in this way includes the large volume of binder absorbed by such aggregate. Defining VMA in this way is a non-standard practice and can result in mixtures that are deficient in asphalt binder, difficult to place and compact, and prone to fatigue cracking. Voids Filled with Asphalt Voids filled with asphalt (VFA) is the percentage of VMA filled with asphalt binderâthe balance is air voids. An asphalt concrete mixture with a VMA of 16% and an effective asphalt content of 12% has a VFA value of (12/16) Ã 100% = 75%. In this case, 25% of the VMA is air voids. Consider a second mixture, with 15% VMA and 5% air voids. The effective asphalt content is then 15 â 5 = 10%, and the VFA is (10/15) Ã 100% = 67%. VFA is calculated by dividing the effective binder content by the VMA and multiplying by 100%. In designing asphalt concrete mixtures, VFA is closely related to both VMA and Vbe. This is because with the design air void content constant at about 4.0%, as VMA increases, Vbe increases and VFA also increases. Therefore, in most cases VFA should be thought of as simply an indicator of mix richness, like VMA or Vbe. If design voids are fixed or allowed to vary only over a narrow range, there is little point in simultaneously controlling VMA, Vbe, and/or VFA. In fact, simul- taneous control of strongly interrelated volumetric factors can lead to confusion and conflict during the mix design process and during construction. Figure 5-5 shows the relationships between air void content, VFA, and VMA (Figure 5-5a) and Vbe (Figure 5-5b). It is not entirely clear what aspects of performance are related to VFA that are not also strongly related to other volumetric factors, especially Vbe. Some engineers have proposed that fatigue resistance increases with increasing VFA. However, VFA and Vbe are strongly related. Recent research strongly suggests that Vbe is a somewhat better overall indicator of fatigue resist- ance in asphalt concrete mixtures. Therefore, in order to control or evaluate fatigue resistance, engineers and technicians should either use Vbe, or VMA at a constant design air void content. There is then little need to independently specify VFA. Relationships between mixture compo- sition and performance are discussed in more detail in Chapter 6 of this manual. Apparent Film Thickness âFilm thickness,â when applied to asphalt concrete mixtures, refers to the average thickness of binder coating aggregate particles in the mixture. Some engineers and researchers have proposed that this is an important characteristic related to several aspects of pavement performanceâ mixtures with low film thickness will be brittle and prone to durability problems, while mixtures with high film thickness will have too much asphalt and may be prone to rutting and shoving. Film thickness is, however, a controversial concept among paving engineers. Many engineers strongly oppose the use of this term, since there are, in fact, no real films of asphalt binder within an asphalt concrete mixture; the asphalt binder exists as a single homogenous phase binding the aggregate particles together. Critics of film thickness point out that there is no way to physically Mixture Volumetric Composition 51
separate an aggregate particle with an intact asphalt binder film from a compacted asphalt con- crete mixture. However, this criticism does not address the issue of whether or not calculated film thickness values are correlated to pavement performance. For this reason, it is suggested that engineers and technicians use the term âapparent film thicknessâ rather than âfilm thickness,â thereby avoiding the main objection of many critics that such films do not physically exist. Figure 5-6 illustrates the concept of apparent film thickness. Recent research (documented in NCHRP Report 567) strongly suggests that there are reasons why apparent film thickness should relate to performance, especially rut resistance. Rut resistance of asphalt concrete mixtures increases as VMA decreases and aggregate fineness increases. Because binder content decreases with decreasing VMA, this means that rut resistance should increase 52 A Manual for Design of Hot Mix Asphalt with Commentary 40 50 60 70 80 90 100 5 10 15 20 25 VMA, Volume % VF A , % 3% 5% 4% (a) 40 50 60 70 80 90 0 5 10 15 20 Vbe, Volume % VF A , % 3% 5% 4% (b) Figure 5-5. Relationship between air void content (labels to the left of curves), VFA and (a) VMA, and (b) Vbe. aggregate aggregate aggregate asphalt asphalt as ph al t absorbed asphalt ab so rb ed as ph alt fil m th ic kn es s air vo id Figure 5-6. Concept of apparent film thickness. Calculation of apparent film thickness should not include asphalt binder absorbed by the aggregate.
with decreasing apparent film thickness, as has been suggested by many engineers and observed in various field studies. However, the relationship between rut resistance and film thickness is not an inherent mechanism of asphalt films, but instead appears to be an indirect but useful relationship. NCHRP Report 567 suggests that HMA mixtures with apparent film thickness values greater than 9 to 10 microns can be prone to excessive rutting. Although physically distinct films of asphalt binder cannot be separated from a compacted specimen of asphalt concrete, such films do have physical meaning in loose uncompacted HMA. Furthermore, these films serve an important purposeâthey lubricate the aggregate particles and allow the HMA to be placed and compacted properly. Apparent film thickness values that are too low are indicative of mixtures that are difficult to place and compact, which in turn can cause segregation, high in-place air void content, and a pavement that is permeable and prone to raveling and surface cracking. Again, this relationship is not a direct one; the lack of durability is not the result of low film thickness, but of segregation and/or poor compaction brought about by the poor workability resulting from low film thickness in the loose hot mix. Unfortunately, research linking apparent film thickness to the workability of HMA has not yet been performed. Different ranges for minimum apparent film thickness have been suggested since this concept was first proposed. It is suggested that mixtures with values below about 6 to 7 microns may be difficult to place and compact properly. The discussion above suggests that apparent film thickness can be a useful tool for designing and analyzing asphalt concrete mixtures. Film thickness values in the range of 7 to 9 microns appear to provide the best compromise between workability and rut resistance. Values below 6 microns or above 10 microns should be avoided. Although apparent film thickness is a poten- tially useful concept, the relationships between apparent film thickness and performance are, at best, indirect. Furthermore, equally good means of controlling mixture composition as it relates to performance are available that do not involve the use of apparent film thickness. Controlling VMA, design air void content, and aggregate fines is essentially equivalent to controlling film thickness. Agencies that choose to specify film thickness for asphalt concrete mixtures should take special care to ensure that there are no unintended conflicts with any simultaneous requirements for VMA, design air void content, or aggregate gradation. Mixture-Specific Gravity Specific gravity has the same meaning when applied to asphalt concrete mixtures as it does when applied to aggregates and other materialsâthe ratio of the density of a material to the density of water at 25Â°C and at standard air pressure. Because the density of water under these conditions is 1.000 gm/cm3, specific gravity is interchangeable with density in these circumstances. However, specific gravity, since it is a ratio, is dimensionless. A mixture with a bulk specific gravity of 1.352 has a bulk density of 1.352 g/cm3. Some agencies use density in units of kg/m3, which will be 1,000 Ã the specific gravity. The specific gravity of the mixture in the previous example could be given as 1.352 g/cm3 or 1,352 kg/m3. There is no link between specific gravity and performance. However, measuring and calculating specific gravity and understanding how specific gravity is used in volumetric analysis is critical to developing asphalt concrete mix designs and analyzing paving mixtures. Bulk Specific Gravity The bulk specific gravity of a mixture refers to the specific gravity of a specimen of compacted mixture, including the volume of air voids within the mixture. It is equivalent to the mass of a given specimen in grams, divided by its total volume in cubic centimeters. The bulk specific gravity Mixture Volumetric Composition 53
of an asphalt concrete mixture can be determined using either laboratory-compacted specimens or cores or slabs cut from a pavement. The standard procedure for determining the bulk specific gravity of compacted asphalt concrete involves weighing the specimen in air and in water. Two slightly different laboratory techniques are used, depending on the absorption of the specimen. For low absorption (less than 2.0%), saturated surface-dry specimens are used (AASHTO T 166). For specimens having high absorption, paraffin-coated specimens should be used in the specific gravity determination (AASHTO T 275). The following formula is used for calculating bulk specific gravity of a saturated surface-dry specimen: where Gmb = bulk specific gravity of compacted specimen A = mass of the dry specimen in air, g B = mass of the saturated surface-dry specimen in air, g, and C = mass of the specimen in water, g As a general rule, if the water absorption of a compacted HMA mixture is above 2.0%, the bulk specific gravity should be determined using paraffin-coated specimens. The calculation of specific gravity in this case is more complicated because the mass and volume of the paraffin film must be accounted for; details can be found in AASHTO T 275. Figure 5-7 is a sketch of a typical weight-in-water determination. Some agencies determine mixture bulk specific gravity using a pycnometer method, which involves calibrating a container and then determining the weight of the container with the compacted specimen and filled with water. Although theoretically this method will provide results equivalent to the weight-in-water method, no AASHTO standard exists for this procedure. Furthermore, use of multiple procedures for determining specific gravity of aggregates and HMA mixtures should be discouraged, since this can only increase the variability in the test results and in the subsequent volumetric analyses. Theoretical Maximum Specific Gravity The theoretical maximum specific gravity of an asphalt concrete mixture is the specific gravity of the mixture at zero air void content. It is one of the most difficult tests performed in paving materials laboratories and also one of the most important. Like bulk specific gravity, G A B C mb = â ( )5 1- 54 A Manual for Design of Hot Mix Asphalt with Commentary Electronic balance Wire hook Mesh basket Tub filled with distilled water Compacted specimen Figure 5-7. Determining weight in water of compacted specimen of HMA.
theoretical maximum specific gravity in and of itself does not affect the performance of a paving mixture. However, it is essential in determining volumetric factors that are good indicators of performance, such as air void content and VMA. Maximum specific gravity is determined by measuring the specific gravity of the loose paving mixture, after removing all of the air entrapped in the mixture by subjecting the mixture to a partial vacuum (vacuum saturation). The loose mix is prepared by gently heating the sample in an oven until it can be easily broken apart. The mixture is then removed from the oven and occasionally stirred while cooling, to make sure that it remains broken up as much as possi- ble into separate particles of asphalt-coated aggregate. After determining the weight in air of the sample, it is placed in a tared, calibrated vacuum container. The container is then con- nected to a vacuum pump, and the pressure in the container gradually reduced to 30 mm Hg or lessâabout 4% of normal atmospheric pressure. This partial vacuum is maintained for 5 to 15 minutes, and the container is occasionally tapped or rolled to help release entrapped air from the loose mixture. The vacuum is then carefully released, the container topped off with water to the calibration mark, and the weight of the container, specimen, and water determined. The theoretical maximum specific gravity of the specimen is calculated using the following formula: where Gmm = theoretical maximum specific gravity of loose mixture A = mass of oven-dry specimen in air, g D = mass of container filled with water at 25Â°C to calibration mark, g E = mass of container with specimen filled with water at 25Â°C to calibration mark, g Because of the importance of theoretical maximum specific gravity determinations, and because the measurements are difficult to perform with great precision, some additional comments concerning this procedure are warranted. In a well-run laboratory, every effort should be made to perform this procedure as much as possible in the same way every time it is run. Many laboratories use small sieve shakers to agitate the specimen while the vacuum is applied, because of the variability in hand rolling and tapping. Although the procedure allows for a time range of 5 to 15 minutes for vacuum saturation, a much narrower time range should be used. Initial tests with typical local materials and with the specific vacuum saturation equipment to be used in running the procedure will help determine the most effective time for applying the vacuum. Because this test involves pulling a vacuum on a container filled with water, care should be made to ensure that the pump is suitable for this use. Many vacuum pumps are quickly damaged by water vapor when water condenses within the interior of the pump, mixing with the vacuum oil and ruining its effectiveness. If such a pump is not available, a series of traps should be installed between the specimen and the pump to prevent water vapor from entering the pump. Because water will boil at 30 mm Hg at a temperature of 29Â°C (84Â°F), the area in which this test is performed and the water used in the procedure should be kept cool. It will be impossible to reach a vacuum of 30 mm Hg if the temperature of the water within the container is 84Â°F or higher. Laboratory personnel should also make certain that the pump used can quickly reach a partial vacuum of at least 30 mm Hg. Good-quality, accurately calibrated gages should be used to monitor the vacuum during the procedure. The complete procedure for performing the theoretical maximum specific gravity test can be found in AASHTO T 209. Figure 5-8 is a diagram of a sample of loose mix being vacuum saturated as part of this procedure. G A A D E mm = + â ( )5 2- Mixture Volumetric Composition 55
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 56 A Manual for Design of Hot Mix Asphalt with Commentary vacuum container vapor traps calibrated gage vacuum pump 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.
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 voidsâ 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: 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 G P P P P G P G sb s A s A s A s A sb s A s = + + + â ââ â â â + 1 2 3 1 1 2 . . . b s A sb P G2 3 3 5 3â ââ â â â + â ââ â â â + . . . ( )- Mixture Volumetric Composition 57 ai r aspha lt bi nde r absorbed asphalt a ggr egat e be V ba V sb V b V se V mm V mb V a V VMA V be = Volume of effective asphalt binder VBE = Effective asphalt content, percent by volume V ba = Volume of absorbed asphalt binder VBA = Absorbed asphalt binder, percent by total mix volume V ma = Volume of voids in mineral aggregate VMA = Voids in mineral aggregate, percent by volume V sb = Volume of aggregate, bulk (including all permeable surface pores) V b = Volume of asphalt binder, total VB = Total asphalt binder content, percent by volume V se = Volume of aggregate, effective (excluding surface pores filled with asphalt) V a = Volume of air voids VA = Air void content, volume percent V mm = Volume of aggregate and asphalt V mb = Volume of specimen, total Figure 5-9. Definition of volume terms used in volumetric analysis.
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: 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: 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: 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: where VBA = Absorbed asphalt content, % by total mixture volume Gmb = Bulk specific gravity of the mixture VBA G P G P G G mb b b s sb mm = âââ ââ â + âââ ââ â â âââ ââ ââ¡ 100 â£â¢ â¤ â¦â¥ ( )5 7- VB P G G b mb b = ( )5 6- P M M M b b s b = + âââ ââ â100 5 5( )- VA G G mb mm = â âââ ââ ââ¡â£â¢ â¤ â¦â¥100 1 5 4( )- 58 A Manual for Design of Hot Mix Asphalt with Commentary
Pb = Total asphalt binder content, % by mix mass Gb = Specific gravity of the asphalt binder Ps = Total aggregate content, % by mix mass = 100 â 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: 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: 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: 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: where VFA is the voids filled with asphalt, as a volume percentage. VFA VBE VMA = âââ ââ â100 5 12( )- VMA VA VBE= + ( )5 11- P P Pba b be= â ( )5 10- P P VBE VB be b= âââ ââ â ( )5 9- VBE VB VBA= â ( )5 8- Mixture Volumetric Composition 59
Apparent Film Thickness. Apparent film thickness can be calculated using the following formula: where AFT = Apparent film thickness, Âµm 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 â 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 valuesâthey 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: 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: 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. S G P P P P s sb = âââ ââ â â( )+ â 1 1 000 1 4 2 050 37 5 37 5 , . .. . 25 25 19 5 19 5 12 5 1 2 8 3 9 5 5 ( )+ â( )+ â( ) + . . . . . .P P P P P 2 5 9 5 9 5 4 75 4 75 2 368 9 17 9. . . . . .. .â( )+ â( )+ âP P P P P( ) + â( )+ â( )+36 0 71 3 1412 36 1 18 1 18 0 60. .. . . .P P P P P P P P P P 0 60 0 30 0 30 0 15 0 15 0283 566 . . . . . â( ) + â( )+ â . ., ( ) 075 0 0751 600 5 15 ( )+ ( ) â¡ â£ â¢â¢â¢â¢â¢â¢ â¤ â¦ â¥â¥â¥â¥â¥â¥P - S P P P s â + +0 30 0 15 0 075 5 5 14. . . ( )- AFT VBE S PGs s mb = 1 000 5 13 , ( )- 60 A Manual for Design of Hot Mix Asphalt with Commentary
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. (continued on next page) Material Specific Gravity Percent by Mass in Aggregate Blend Percent by Mass in 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 5-1. Mixture composition 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 5-2. Gradation 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 Table 5-3. Mixture bulk and maximum specific gravity data for example problem.
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: Step 2. Determine the mixture bulk specific gravity using Equation 5-1: Step 3. Determine the mixture maximum specific gravity using Equation 5-2: Step 4. Calculate the air void content using Equation 5-4: Step 5. Calculate the total asphalt binder content by mix volume using Equation 5-6: Step 6. Calculate the absorbed asphalt binder content by mix volume using Equation 5-7: Step 7. Calculate the effective asphalt binder content by volume by subtracting the absorbed asphalt from the total asphalt content (Equation 5-8): Step 8. Calculate the effective and absorbed asphalt contents by total mix weight using Equations 5-9 and 5-10: Pba = â =4 9 4 7 0 2. . . % Pbe = â ââ â â â =4 9 10 7 11 2 4 7. . . . % VBE = â =11 2 0 5 10 7. . . % VBA = â ââ â â â + â ââ â â â â2 357 4 9 1 03 95 1 2 622 100 2 . . . . . . . % 451 0 5 â ââ â â â â¡ â£â¢ â¤ â¦â¥ = VB = Ã = 4 9 2 357 1 03 11 2 . . . . % VA = â â ââ â â â â¡ â£â¢ â¤ â¦â¥ =100 1 2 357 2 451 3 8 . . . % Gmm = + â = 4 295 0 4 295 0 7 823 1 10 365 5 2 451 , . , . , . , . . Gmb = â = 4 299 3 4 333 7 2 510 0 2 357 , . , . , . . Gsb = + + â ââ â â â + â ââ â â â + 28 28 44 28 2 621 28 2 668 44 2. . . . 595 2 622â ââ â â â =
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): Step 10. Calculate the VFA using Equation 5-12: Step 11. Estimate the specific surface of aggregate using Equation 5-14: Step 12. Calculate the apparent film thickness using Equation 5-13: Table 5-4 summarizes the results of the volumetric analysis example problem. AFT = Ã Ã Ã = 1 000 10 7 5 1 95 1 2 357 9 4 , . . . . . Î¼m Ss â + + = 11 9 5 5 5 5 1 . . m kg2 VFA = â ââ â â â =100 10 7 14 5 73 8 . . . % VMA = + =3 8 10 7 14 5. . . % 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, Î¼m 9.4 Table 5-4. Summary of volumetric analysis example problem. 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
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. 64 A Manual for Design of Hot Mix Asphalt with Commentary