Question 5 of 6: Aggregate Moisture, Superpave Gradation Terms and HMA Volumetrics

Question 5: Aggregate Moisture, Superpave Gradation Terms and HMA Volumetrics (6 + 4 + 10 = 20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Part (a) — Free water in the wet aggregate (6 marks)

Given. Weight of wet aggregate $W_{\text{wet}} = 300.0$ N; oven-dry weight $W_{\text{dry}} = 280.0$ N; absorption capacity $= 3.0$ per cent of the oven-dry weight.

Find. The free (surface) moisture, expressed as a percentage.

Approach. Total water in the sample is the difference between the wet and oven-dry weights. Part of that water is held inside the aggregate pores — that is the absorption — and the remainder is the free water clinging to the particle surfaces. Both moisture content and absorption are conventionally referred to the oven-dry weight, so free water is simply their difference.

1. Total water present. The water carried by the sample is the weight it loses on oven drying: $$W_{\text{water}}=W_{\text{wet}}-W_{\text{dry}}=300.0-280.0=20.0\ \text{N}$$
2. Total moisture content on the oven-dry basis. By definition, $$MC=\frac{W_{\text{wet}}-W_{\text{dry}}}{W_{\text{dry}}}\times100=\frac{20.0}{280.0}\times100=7.143\ \text{per cent}$$ Note the denominator: the dry weight, not the wet weight. Using 300.0 N here is the single most common error in this calculation.
3. Water held by absorption. The aggregate can absorb 3.0 per cent of its oven-dry weight, so at saturated surface-dry condition it holds $$W_{\text{abs}}=0.030\times280.0=8.4\ \text{N}$$ The sample's moisture content of 7.143 per cent exceeds the 3.0 per cent absorption, which confirms that the aggregate is wetter than saturated surface-dry and that free water is indeed present.
4. Free (surface) water, as a percentage of the oven-dry weight. Subtracting the absorbed portion from the total, $$\text{Free water}=MC-\text{absorption}=7.143-3.0=\boxed{4.143\ \text{per cent}}$$
5. The same result as a weight, and on the wet basis. In weight terms $$W_{\text{free}}=20.0-8.4=11.6\ \text{N}$$ and expressed as a fraction of the original wet sample this is $11.6/300.0\times100=3.867$ per cent. The dry-basis figure of 4.143 per cent is the standard answer, because that is the basis on which both moisture content and absorption are defined; the 3.867 per cent figure is quoted here only because the question's phrase "in the original wet sample" could be read that way. A one-line statement of the basis on the answer paper removes the ambiguity.
6. Why the number matters on site. Free water is the correction applied to a concrete or asphalt batch: 11.6 N of the aggregate weight is water that must be deducted from the mixing water added at the plant, and the aggregate must be batched at 300.0 N rather than 280.0 N to deliver the required weight of solids. Absorbed water, by contrast, is already inside the particle and takes no part in the mix.

Part (b) — Four Superpave gradation terms (4 marks)

Maximum size. In Superpave, the maximum size of an aggregate is one sieve size larger than the nominal maximum size. It is the smallest sieve through which 100 per cent of the aggregate must pass. For a 12.5 mm nominal maximum size mix, the maximum size is 19.0 mm. Note that this definition differs from the ASTM C125 convention used for concrete aggregates, where the maximum size is the smallest sieve through which the whole sample passes; Superpave defines both terms one sieve coarser.

Nominal maximum size (NMAS). One sieve size larger than the first sieve to retain more than 10 per cent of the aggregate. It is the sieve that names the mix — a "12.5 mm Superpave mix" — and it governs the minimum permitted VMA, the control-point limits, the restricted-zone position (in the original method), and the minimum lift thickness, which should be at least three to four times the NMAS.

Maximum density line. On a 0.45-power gradation chart — percent passing on a linear vertical axis against sieve opening raised to the power 0.45 on the horizontal axis — the maximum density line is the straight line from the origin to 100 per cent passing at the maximum aggregate size. It represents the Fuller and Thompson gradation $P = 100(d/D)^{0.45}$, which packs the aggregate to its greatest possible density and therefore its least void space. A mix graded exactly along it would have almost no room for binder, so practical gradations are deliberately kept off it — usually slightly above it in the fine sizes (a fine-graded mix) or below it (a coarse-graded mix) — in order to develop the VMA the mix needs.

Primary control sieve (PCS) control point. Superpave classifies a gradation as fine-graded or coarse-graded by the percentage passing a single designated sieve, the primary control sieve, which is defined as the sieve nearest to $0.22\times NMAS$ (for example 2.36 mm for a 12.5 mm mix, 4.75 mm for a 19.0 mm mix). The PCS control point is the percent-passing value at that sieve that separates the two classes: if the gradation passes more than the control-point value it is fine-graded and plots above the maximum density line; if it passes less it is coarse-graded. The distinction matters because coarse-graded mixes rely more on stone-on-stone contact and behave differently in compaction and in rutting. In the current Superpave method the control points at the NMAS, the PCS and the 0.075 mm sieve replace the older "restricted zone", which has been withdrawn.

Part (c) — Volumetric properties of the compacted mix (10 marks)

Given.

Find. Bulk density of the compacted mix, air voids $V_a$, voids in the mineral aggregate VMA, voids filled with asphalt VFA, and the dust proportion DP.

Approach. Take a unit weight of mix and express each phase — aggregate, binder and air — as a volume using its specific gravity. Air voids follow from the difference between the compacted and the void-free specific gravities; VMA is everything that is not aggregate volume; VFA is the fraction of VMA occupied by binder; and DP compares the mineral filler with the effective binder.

1. Check the internal consistency of the given data first. The maximum specific gravity can be recomputed from the component specific gravities: $$G_{mm}=\frac{100}{\dfrac{P_s}{G_{se}}+\dfrac{P_b}{G_b}}=\frac{100}{\dfrac{95.0}{2.726}+\dfrac{5.0}{1.030}}=\frac{100}{34.850+4.854}=\frac{100}{39.704}=2.519$$ This agrees with the measured 2.520 to within 0.06 per cent, so the data set is consistent and either value may be used. The measured 2.520 is carried forward.
2. Bulk density of the compacted mix. Density is the bulk specific gravity times the density of water: $$\rho=G_{mb}\times\rho_w=2.360\times1000=\boxed{2360\ \text{kg/m}^3}$$ that is 2.360 Mg/m³, or 147.3 lb/ft³. (Using the density of water at 25 °C, 997 kg/m³, gives 2353 kg/m³; the difference is immaterial and 1000 kg/m³ is the convention.)
3. Air voids in the compacted mix. $G_{mm}$ describes the same mix with zero air, so the air volume is the fractional difference between the two specific gravities: $$V_a=100\times\frac{G_{mm}-G_{mb}}{G_{mm}}=100\times\frac{2.520-2.360}{2.520}=100\times\frac{0.160}{2.520}=\boxed{6.35\ \text{per cent}}$$ This is well above the 4 per cent Superpave design target, so the specimen is under-compacted or the binder content is below optimum — a point worth making in the answer.
4. Voids in the mineral aggregate. VMA is the total void volume between the aggregate particles in the compacted mix, that is the air plus the effective binder, expressed as a percentage of the bulk volume. It is defined using the bulk specific gravity of the aggregate, $G_{sb}$: $$VMA=100-\frac{G_{mb}\,P_s}{G_{sb}}$$ The paper does not give $G_{sb}$, only $G_{se}$. Under Note 2, $G_{sb}$ is taken equal to $G_{se}=2.726$, which is equivalent to assuming that the aggregate absorbs no binder ($P_{ba}=0$). Then $$VMA=100-\frac{2.360\times95.0}{2.726}=100-\frac{224.20}{2.726}=100-82.25=\boxed{17.75\ \text{per cent}}$$ The paper does not state the nominal maximum size, but this comfortably exceeds the Superpave minimum for any common surface or binder mix (13 per cent at 19 mm, 14 per cent at 12.5 mm, 15 per cent at 9.5 mm NMAS).
5. Voids filled with asphalt. VFA is the percentage of the VMA that the effective binder occupies: $$VFA=100\times\frac{VMA-V_a}{VMA}=100\times\frac{17.75-6.35}{17.75}=100\times\frac{11.41}{17.75}=\boxed{64.2\ \text{per cent}}$$ For heavy traffic the Superpave range is 65 to 75 per cent, so at 64.2 per cent this mix is marginally lean — consistent with the high air void content found in step 3.
6. Cross-check by the volumetric identity. VMA must equal the air voids plus the effective binder volume. With $P_{ba}=0$ the effective binder content equals the total binder content, $P_{be}=5.0$ per cent, whose volume fraction is $$V_{be}=\frac{P_{be}\,G_{mb}}{G_b}=\frac{5.0\times2.360}{1.030}=11.46\ \text{per cent}$$ Adding the air voids computed on the consistent $G_{mm}=2.519$, namely 6.30 per cent, gives $6.30+11.46=17.75$ per cent, which reproduces the VMA exactly. The identity closes, so the arithmetic is sound.
7. Dust proportion. DP is the ratio of the mineral filler passing 0.075 mm to the effective binder content, both as percentages of the total mix: $$DP=\frac{P_{0.075}}{P_{be}}=\frac{5.3}{5.0}=\boxed{1.06}$$ The Superpave acceptable range is 0.6 to 1.2 (extended to 1.6 for coarse-graded mixes), so 1.06 is satisfactory, though it sits in the upper half of the band and any increase in baghouse fines would push the mix towards a stiff, brittle mastic.