The volumetric relationship in an asphalt mixture is shown schematically in Figure 7.1 in German terms. Equations are based on TP A-08 2007 and Hutschenreuther and Woerner (2000).
Symbols in Figure 7.1 include the following:
Hbit = Volume of voids in compacted asphalt samples, % (v/v)
Bv = Binder volume, % (v/v)
Mv = Mineral aggregate volume, % (v/v)
HMbit = Voids in mineral aggregate (VMA), % (v/v)
Obviously, the sum of all the parts should equal 100%.
MV + BV + Hbit = 100%
The way of calculating volume parameters and defining them is outlined here.
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Air voids
Aggregate volume
Mv
FIGURE 7.1 Volume relationship in an asphalt mixture according to terminology adopted in Germany. (From Graf, K., Splittmastixasphalt—Anwendung und Bewahrung. Rettenmaier Seminar eSeMA’06. Zakopane [Poland], 2006. With permission.)
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The binder volume in an asphalt mixture
В = Binder content in the mixture, % (m/m)
pA = Bulk density of the asphalt mixture (sample), g/cm3
pB = Binder density at a temperature of 25°C, g/cm3
Volume of mineral aggregate
Pa (100 — В)
pR, M
pA = Bulk density of the asphalt mixture (sample), g/cm3 В = Binder content in the mixture, % (m/m) pRM = Density of the aggregate mix, g/cm3
Content of air voids in compacted asphalt mixture
Hbit = PR-bit Pa -100%
PR, bit
pA = Bulk density of the asphalt mixture (in German Raumdichte), g/cm3 pRbit = Maximum density of the asphalt mixture (in German Rohdichte), g/cm3
Air voids in compacted mineral aggregate (the hypothetical voids content)
HM, bit = Hbit + BV
Bv = Binder volume, % (v/v)
Hbit = Air voids in the compacted asphalt mixture, % (v/v) Voids filled with a binder
hfb = -^- • 100%
HM, bit
Bv = Binder volume, % (v/v) HM, bit = VMA, % (v/v)
7.1.3 Comments
• In most cases of designing an SMA, the steps described in Section 7.1.1 are sufficient.
• The void contents in compacted Marshall specimens after the application of various compactive efforts (2 x 50 and 2 x 75 blows [Graf, 2006]) have also been compared. For a designer, a large difference between samples of the same SMA mixture under different compactive efforts is an indicator of too high a compactability under the influence of an excessive effort. However, that practice has not been formalized.
• Some German engineers check the voids in mineral aggregate (HMbit) to find out if it is higher than 18% (v/v), as do their fellow U. S. engineers. However, this practice remains unsanctioned.
