Background

The particle size distribution, or gradation, of the constituent aggregate (Figure 3) is one of the most influential characteristics in determining how an HMA mixture will perform as a pavement material. Aggregate gradation influences almost every important HMA property including stiffness, stability, durability, permeability, workability, fatigue resistance, skid resistance and resistance to moisture damage (Roberts et al., 1996).

Gradation Graphs

Gradation is often expressed in graphical form. Typically gradation graphs use concepts of maximum density gradation and its expression in equation form to plot a special graph referred to as the FHWA 0.45 power graph.

Maximum Density Gradation

Theoretically, there exists a particular gradation that, for a given maximum aggregate size, will produce the maximum density. This gradation would involve a particle arrangement where successively smaller particles are packed within the voids between larger particles (Figure 4). If done ideally, this would result in a minimum void space between particles and produce a maximum density. Practically, an aggregate gradation of maximum density is not desired because a certain amount of void space is required to provide adequate volume for the asphalt binder to occupy.

Fuller and Thompson's Equation (Interactive Equation)

Regardless of its practical use, a maximum density gradation provides a convenient reference. In 1907, Fuller and Thompson developed a widely used equation to describe a maximum density gradation for a given maximum aggregate size. This equation is:

Where:	P	=	percent finer than an aggregate size
	d	=	aggregate size being considered
	D	=	maximum aggregate size
	n	=	parameter which adjusts curve for fineness or coarseness (for maximum particle density n ≈ 0.5 according to Fuller and Thompson)

The 0.45 Power Maximum Density Graph (see Graph)

In the early 1960s, the FHWA introduced the standard gradation graph used in the HMA industry today. This graph uses Fuller and Thompson's equation with n = 0.45 and is convenient for determining the maximum density line and adjusting gradation (Roberts et al., 1996). This graph is slightly different than other gradation graphs because it uses the sieve size raised to the n^th power (usually 0.45) as the x-axis units. Thus, a plot of Fuller and Thompson's maximum density equation with n = 0.45 appears as a straight diagonal line. This straight line goes from zero to the maximum aggregate size for the gradation being considered. There is some debate as to whether this line should end at maximum aggregate size or nominal maximum aggregate size or somewhere in between, however the most commonly accepted practice is to end it at the maximum aggregate size.

Gradation Types (see Graph)

Aggregate gradation can be generally described by a few broadly defined gradation categories; each one describing a general type of gradation. These categories are:

• Dense or well-graded. Refers to a gradation that is near the FHWA’s 0.45 power curve for maximum density. The most common HMA mix designs in the U.S. tend to use dense graded aggregate. Typical gradations are near the 0.45 power curve but not right on it. Generally, a true maximum density gradation (exactly on the 0.45 power curve) would result in unacceptably low VMA.
• Gap graded. Refers to a gradation that contains only a small percentage of aggregate particles in the mid-size range. The curve is flat in the mid-size range. Gap graded mixes can be prone to segregation during placement. Stone matrix asphalt (SMA) is a gap graded HMA.
• Open graded. Refers to a gradation that contains only a small percentage of aggregate particles in the small range. This results in more air voids because there are not enough small particles to fill in the voids between the larger particles. The curve is near vertical in the mid-size range, and flat and near-zero in the small-size range.
• Uniformly graded. Refers to a gradation that contains most of the particles in a very narrow size range. In essence, all the particles are the same size. The curve is steep and only occupies the narrow size range specified.

The desired gradation for a particular HMA mixture is dependent upon its intended use and desired characteristics, predicted loading, environmental conditions, as well as material, structural and mix properties. Therefore, gradation requirements for specific HMA mixtures can vary widely. The vast majority of the HMA placed in the U.S. is dense-graded.

Maximum Aggregate Size

Maximum aggregate size can affect HMA in several ways. Instability (rutting, shoving) may result from excessively small maximum sizes; and poor workability and/or segregation may result from excessively large maximum sizes (Roberts et al., 1996). Maximum aggregate size can be defined in two different ways:

• Maximum aggregate size. The smallest sieve through which 100 percent of the aggregate sample particles pass. Superpave mix design defines the maximum aggregate size as "one sieve larger than the nominal maximum size" (Roberts et al., 1996).
• Nominal maximum aggregate size (NMAS). The largest sieve that retains some of the aggregate particles but generally not more than 10 percent by weight. Superpave mix design defines nominal maximum aggregate size as "one sieve size larger than the first sieve to retain more than 10 percent of the material" (Roberts et al., 1996).

These two definitions will likely give different sizes for the same aggregate sample. Therefore, it is important to specify whether "maximum size" or "nominal maximum size" is being referenced.

Other Gradation Terms (see Graph)

• Fine gradation. A gradation that, when plotted on the 0.45 power gradation graph, falls mostly above the 0.45 power maximum density line. The term generally applies to dense graded aggregate.
• Coarse gradation. A gradation that, when plotted on the 0.45 power gradation graph, falls mostly below the 0.45 power maximum density line. The term generally applies to dense graded aggregate.
• Fine aggregate (sometimes just referred to as "fines"). Defined by the Asphalt Institute (2001) as the fraction of aggregate passing the 2.36 mm (No. 8) sieve. Defined by AASHTO M 147 as natural or crushed sand passing the No. 10 (2.00 mm) sieve and mineral particles passing the No. 200 (0.075 mm) sieve.
• Coarse aggregate. Defined by the Asphalt Institute (2001) as the fraction of aggregate retained on the No. 8 (2.36 mm) sieve. Defined by AASHTO M 147 as hard, durable particles or fragments of stone, gravel or slag retained on the No. 10 (2.00 mm) sieve.
• Mineral filler. Defined by the Asphalt Institute (2001) as the fraction of fine aggregate the passes the No. 30 (0.60 mm) sieve. This is not universally accepted; some organizations define "mineral filler" as passing the No. 200 (0.075 mm) sieve (this is actually the definition for "mineral dust" in the VSL). Pulverized limestone is the most commonly manufactured mineral filler, although other stone dust, silica, hydrated lime, portland cement and certain natural deposits of finely divided mineral matter are also used (Asphalt Institute, 1962).
• Mineral dust. Defined by the Asphalt Institute (2001) as the fraction of fine aggregate that passes the No. 200 (0.075 mm) sieve.

• Restricted zone. A term associated with Superpave mix design that referred to a defined zone on the FHWA’s 0.45 power gradation graph. Originally, it was observed that mixes closely following the 0.45 power maximum density line in the finer gradations sometimes had unacceptably low VMA typically due to an excess of natural sand. Therefore, in an attempt to minimize this problem, Superpave mix design included a restricted zone through which a typical gradation should not pass as a recommended guideline. However, since the restricted zone's original inception, NCHRP Report 464: The Restricted Zone in the Superpave Aggregate Gradation Specification has concluded that "...gradations that violated the restricted zone performed similarly to or better than the mixes having gradations passing outside the restricted zone; therefore, the restricted zone requirement is redundant for mixes meeting all Superpave volumetric parameters...It has been recommended to delete references to the restricted zone as either a requirement or a guideline from the AASHTO specification (AASHTO M 323) and practice (AASHTO R 35) for Superpave mix design." (Kandhal and Cooley, 2001). The restricted zone remains in Superpave as "guidance" only.

Gradation Specification

Gradation and size are specified by designating a NMAS and a series of gradation control points. Control points give the allowable percent passing (or retained) range for given sieve sizes. For instance, the gradation control points for a 0.5 inch (12.5 mm) Superpave mix specify a maximum of 58% passing and a minimum of 28% passing on the No. 8 (2.36 mm) sieve. The Control Points Graph shows aggregate gradation control points (shown as large dots) for Superpave mixes. These gradation control points are quite broad and were included for specific purposes (Huber, 1996):

• 1st control point (minimum 100% passing). Defines the maximum aggregate size for a mix. By definition, 100% must pass this sieve size.
• 2nd control point set (90 to 100% passing). Defines the NMAS for a mix. By definition, 90 to 100% must pass this sieve size.
• 3rd control point set (No. 8 (2.36 mm) sieve). Used to control the amount of sand sized particles in the mixture. The upper control point excludes overly fine mixtures, while the lower control point ensures enough sand sized particles are included to make a dense graded mixture.
• 4th control point set (No. 200 (0.075 mm) sieve). Obtained from ASTM D 3515 as typical for dense graded mixtures. This excludes non-dense graded mixtures such as stone matrix asphalt (SMA), which typically has 10 to 14% passing the No. 200 (0.075 mm) sieve.