Question 4 of 5: Asphalt Concrete Volumetrics and Marshall Mix Design

Question 4: Asphalt Concrete Volumetrics and Marshall Mix Design (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) — The three volumetric definitions (6 marks)

i. Air voids, VTM (voids in the total mix). VTM is the total volume of the small pockets of air trapped between the coated aggregate particles, expressed as a percentage of the bulk volume of the compacted specimen. It is obtained by comparing the bulk specific gravity of the compacted mix with the theoretical maximum specific gravity of the same mix with no air in it at all, VTM = 100(1 − G_mb/G_mm). Its importance is that it is the single most sensitive design parameter: below about 3 % the mix has no room left for the further densification that traffic will impose, so it flushes and ruts, and above about 5 % the void network becomes interconnected, so air and water reach the binder and the mix oxidises, ravels and strips. Design is therefore fixed at 4 % for dense-graded mixtures.

ii. Voids in the mineral aggregate, VMA. VMA is the total volume of the intergranular void space between the aggregate particles in the compacted mixture — that is, the air voids plus the volume of effective (non-absorbed) asphalt — expressed as a percentage of the bulk volume of the specimen, VMA = 100 − G_mbP_s/G_sb. It is the space available for the binder to occupy, so a minimum VMA is specified as a function of nominal maximum aggregate size — 15 % for a 9.5 mm mix, 14 % for 12.5 mm, 13 % for 19 mm, at 4 % design air voids. If VMA is too low the mix simply cannot hold enough asphalt to build a durable film around each particle, no matter how much binder is added, because the extra binder only pushes the air voids down; the fault lies in the aggregate gradation and is cured by changing the grading, not the asphalt content.

iii. Voids filled with asphalt, VFA. VFA is the percentage of the VMA that the effective asphalt actually occupies, VFA = 100(VMA − VTM)/VMA. It is a derived quantity, not an independent one, but it is the parameter that expresses film thickness and hence durability directly: a low VFA means thin, easily oxidised binder films and a dry, ravel-prone mix, while a high VFA means the voids are nearly full, the mix is tender during construction and it will bleed and rut in service. The Asphalt Institute bands VFA by traffic level — roughly 70 to 80 % for light traffic, 65 to 78 % for medium and 65 to 75 % for heavy — the range narrowing and dropping as the traffic becomes more severe.

Part (b) — Marshall design (14 marks)

Given. An AC-30 binder of specific gravity G_b = 1.031; a 9.5 mm nominal maximum size aggregate of bulk specific gravity G_sb = 2.696; a measured theoretical maximum specific gravity G_mm = 2.470 at an asphalt content of 5.0 %; design air voids 4.0 %; Asphalt Institute criteria for medium traffic. The trial-mix averages are:

Find. VTM, VMA and VFA at each trial asphalt content; the design asphalt content that gives 4.0 % air voids; and a check of the stability, flow, VMA and VFA at that asphalt content against the Asphalt Institute medium-traffic criteria.

Approach. Convert the single measured G_mm into an effective aggregate specific gravity, use that to predict G_mm at the other four asphalt contents, compute the three volumetrics at each, interpolate every property to the asphalt content that gives 4.0 % air voids, and test the result against the criteria.

1. Part (b), step 1 — effective specific gravity of the aggregate. Only one $G_{mm}$ was measured, so the aggregate's effective specific gravity is back-calculated from it and then treated as a constant of the aggregate: $$G_{se}=\frac{100-P_{b}}{\dfrac{100}{G_{mm}}-\dfrac{P_{b}}{G_{b}}} =\frac{100-5.0}{\dfrac{100}{2.470}-\dfrac{5.0}{1.031}} =\frac{95}{40.486-4.850}$$ $$\boxed{G_{se}=2.666}$$
2. Part (b), step 2 — theoretical maximum specific gravity at every asphalt content. With $G_{se}$ fixed, $G_{mm}$ at any other binder content follows from the volumes of aggregate and binder in a void-free mix: $$G_{mm}=\frac{100}{\dfrac{100-P_{b}}{G_{se}}+\dfrac{P_{b}}{G_{b}}}$$ which returns 2.5068, 2.4883, 2.4700, 2.4520 and 2.4342 at 4.0, 4.5, 5.0, 5.5 and 6.0 % respectively. The middle value reproduces the measured 2.470 exactly, which is the arithmetic check that step 1 was done correctly.
3. Part (b), step 3 — the three volumetrics at each trial point. Applying the definitions of part (a), $$VTM=100\left(1-\frac{G_{mb}}{G_{mm}}\right),\qquad VMA=100-\frac{G_{mb}\,P_{s}}{G_{sb}},\qquad VFA=100\,\frac{VMA-VTM}{VMA}$$ with $P_{s}=100-P_{b}$. At $P_{b}=4.5\ \%$, for example, $VTM=100(1-2.378/2.4883)=4.43\ \%$, $VMA=100-2.378\times95.5/2.696=15.76\ \%$ and $VFA=100(15.76-4.43)/15.76=71.9\ \%$. The full set is tabulated with the results. Notice that VMA passes through a minimum of about 15.6 % near 5 % binder, which is the characteristic shape and the reason the VMA check is made at the design point rather than at the lowest trial point.
4. Part (b), step 4 — design asphalt content at 4.0 % air voids. Air voids fall monotonically with binder content, from 5.86 % at 4.0 % binder to 0.79 % at 6.0 %, so 4.0 % air voids is bracketed between the 4.5 and 5.0 % trials. Linear interpolation on that interval gives $$P_{b,\text{design}}=4.5+\frac{4.43-4.00}{4.43-3.04}\times(5.0-4.5) =4.5+0.309\times0.5$$ $$\boxed{P_{b,\text{design}}=4.65\ \%\ \text{by mass of mix}}$$
5. Part (b), step 5 — the other properties at the design point. Interpolating every remaining property at the same position between the 4.5 and 5.0 % trials, $$VMA=15.71\ \%,\quad VFA=74.6\ \%,\quad \text{stability}=6.30\ \text{kN},\quad \text{flow}=10.6,\quad G_{mb}=2.383$$ Each is read at the design asphalt content, never at the nearest trial point, because stability and flow both change steeply with binder content in this range.
6. Part (b), step 6 — check against the medium-traffic criteria. The Asphalt Institute criteria for medium traffic, together with the VMA minimum for a 9.5 mm nominal maximum size at 4 % design air voids, are compared with the design values in the table below. Stability exceeds the 5.34 kN minimum by 18 %, flow sits mid-band, VMA clears its 15.0 % floor and VFA sits inside the 65 to 78 % band. $$\boxed{\text{All criteria are satisfied at }P_{b}=4.65\ \%\text{ — the design is acceptable}}$$ The margin on VMA is only 0.7 percentage points, so this mixture is on the edge of being too fine; a small drift in the aggregate gradation towards the fine side would push VMA below 15 % and force a gradation change rather than a binder change.