The aggregate mix used for the design of an asphalt paving concrete consists of 42% coarse aggregates, 51% fine aggregates, and 7% mineral fillers. If the respective bulk specific gravities of these materials are 2.60, 2.71, and 2.69, and the effective specific gravity of the aggregates is 2.82, determine the optimum asphalt content as a percentage of the total mix using results obtained using the Marshall method as shown in the following table. The specific gravity of the asphalt cement is 1.02.

What will be an ideal response?

First, compute the bulk specific gravity and associated bulk density of each

possible mix.

Next, compute VMA for each possible mix using Equation 18.11.

Gbcm and Pta are known for each possible mix; however, Gsb must be computed,

using Equation 18.5, in order to find VMA.

For 5.5% asphalt content:

Gmb = 2.46 Pca = 0.42(94.5) = 39.7

Pta = 94.5 Pfa = 0.51(94.5) = 48.2

Pmf = 0.07(94.5) = 6.6

Gsb = (39.7 + 48.2 + 6.6) / [(39.7/2.60) + (48.2/2.71) + (6.6/2.69)]

Gsb = 2.66

VMA = 100 – (2.46)(94.5) / 2.66

VMA = 12.61%

For 6.0% asphalt content:

Gmb = 2.48 Pca = 0.42(94) = 39.5

Pta = 94 Pfa = 0.51(94) = 47.9

Pmf = 0.07(94) = 6.6

Gsb = (39.5 + 47.9 + 6.6) / [(39.5/2.60) + (47.9/2.71) + (6.6/2.69)]

Gsb = 2.66

VMA = 100 – (2.48)(94) / 2.66

VMA = 12.36%

For 6.5% asphalt content:

Gmb = 2.50 Pca = 0.42(93.5) = 39.3

Pta = 93.5 Pfa = 0.51(93.5) = 47.7

Pmf = 0.07(93.5) = 6.5

Gsb = (39.3 + 47.7 + 6.5) / [(39.3/2.60) + (47.7/2.71) + (6.5/2.69)]

Gsb = 2.66

VMA = 100 – (2.50)(93.5) / 2.66

VMA = 12.12%

For 7.0% asphalt content:

Gmb = 2.50 Pca = 0.42(93) = 39.1

Pta = 93.0 Pfa = 0.51(93) = 47.4

Pmf = 0.07(93) = 6.5

Gsb = (39.1 + 47.4 + 6.5) / [(39.1/2.60) + (47.4/2.71) + (6.5/2.69)]

Gsb = 2.66

VMA = 100 – (2.5)(93) / 2.66

VMA = 12.59%

For 7.5% asphalt content:

Gmb = 2.48 Pca = .42(92.5) = 38.9

Pta = 92.5 Pfa = .51(92.5) = 47.2

Pmf = .07(92.5) = 6.5

Gsb = (38.9 + 47.2 + 6.5) / [(38.9/2.60) + (47.2/2.71) + (6.5/2.69)]

Gsb = 2.66

VMA = 100 – (2.48)(92.5) / 2.66

VMA = 13.76%

Now compute % air voids for each mix using Equation 18.12,

Gmm must be computed using Equation 18.8,

For 5.5% asphalt content:

Gmp = 100 / [(94.5/2.82) + (5.5/1.02)]

Gmp = 2.57

Va = 100 (2.57 – 2.46)/2.57

Va = 4.28%

For 6.0% asphalt content:

Gmp = 100 / [(94.0/2.82) + (6.0/1.02)]

Gmp = 2.55

Va = 100 (2.55 – 2.48)/2.55

Va = 2.75%

For 6.5% asphalt content:

Gmp = 100 / [(93.5/2.82) + (6.5/1.02)]

Gmp = 2.53

Va = 100 (2.53 – 2.5)/2.53

Va = 1.19%

For 7.0% asphalt content:

Gmp = 100 / [(93.0/2.82) + (7.0/1.02)]

Gmp = 2.51

Va = 100 (2.51 – 2.50)/2.51

Va = 0.40%

For 7.5% asphalt content:

Gmp = 100 / [(92.5/2.82) + (7.5/1.02)]

Gmp = 2.49

Va = 100 (2.49 – 2.48)/2.49

Va = 0.40%

Now compute VFA for each mix using Equation 18.13,

For 5.5% asphalt content:

VFA = 100 / [(12.61 – 4.28) /12.61]

VFA = 66.1%

For 6.0% asphalt content:

VFA = 100 / [(12.36 – 2.75) /12.36]

VFA = 77.8%

For 6.5% asphalt content:

VFA = 100 / [(12.12 – 1.19) /12.12]

VFA = 90.2%

For 7.0% asphalt content:

VFA = 100 / [(12.59 – 0.40) /12.59]

VFA = 96.8%

For 7.5% asphalt content:

VFA = 100 / [(13.76 – 0.40) /13.76]

VFA = 97.1%

From these calculations, plot VFA vs. % asphalt, VMA vs. asphalt, Va vs. asphalt.

Also, using the given data, plot stability vs. % asphalt, and flow vs. % asphalt.

At 4% voids, AC is approximately 5.6%

Checking this against the required values in Table 18.7:

At 5.6% AC

Stability ~ 1810

Flow ~ 13

VMA ~ = 12.5%

Assuming medium traffic, this mix is acceptable.