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). The air voids are the small pockets of air distributed among the coated aggregate particles of a compacted paving mixture, expressed as a percentage of the bulk volume of that compacted mixture. Numerically VTM = 100(1 − G_mb/G_mm), where G_mb is the bulk specific gravity of the compacted specimen and G_mm the theoretical maximum specific gravity of the same mixture with no air in it. Air voids are the single most important volumetric property: too few and the mix has no room to densify under traffic, so it flushes and ruts; too many and it is permeable to air and water, so it oxidises, strips and ravels. Design values are 3 to 5 per cent, with 4 per cent the usual target.

ii. Voids in the mineral aggregate, VMA. The VMA is the total volume of intergranular void space between the aggregate particles of a compacted mixture, again as a percentage of the bulk volume; it comprises the air voids plus the volume occupied by the effective (non-absorbed) asphalt. It is computed from the aggregate side only, VMA = 100 − G_mbP_s/G_sb, where P_s is the aggregate content by mass of the mix and G_sb the bulk specific gravity of the aggregate. Its significance is that it is the room available for binder: a mix whose aggregate skeleton packs too tightly leaves no space for a durable binder film, and a specified minimum VMA (a function of nominal maximum aggregate size — 15 per cent for 9.5 mm, 14 per cent for 12.5 mm, 13 per cent for 19 mm at 4 per cent design air voids) is what guarantees a film thick enough to resist oxidation.

iii. Voids filled with asphalt, VFA. The VFA is the percentage of the VMA that the effective asphalt occupies, VFA = 100(VMA − VTM)/VMA. It expresses how full the aggregate voids are of binder rather than air. A low VFA means a thin binder film, a dry, permeable, quickly ageing mix; a high VFA means an over-filled skeleton with too little air reserve, which bleeds and shoves under heavy traffic. The Asphalt Institute range narrows as traffic increases — 70 to 80 per cent for light, 65 to 78 per cent for medium and 65 to 75 per cent for heavy traffic — and together with the VMA minimum it acts as a check that a mix passing the air-void criterion is also durable.

Part (b) — Marshall design asphalt content (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; the theoretical maximum specific gravity of the mixture at 5.0 per cent asphalt, G_mm = 2.470; and the Marshall trial results tabulated below. The mix is to be designed for medium traffic at a design air void content of 4 per cent.

Find. The design asphalt content that satisfies the Asphalt Institute criteria for medium traffic, together with the full volumetric analysis (G_mm, VTM, VMA and VFA at each trial asphalt content) that justifies it.

Approach. Back-calculate the effective specific gravity of the aggregate from the one measured maximum specific gravity, use it to compute G_mm at every trial asphalt content, form VTM, VMA and VFA at each point, read the asphalt content that gives 4 per cent air voids, then check that the stability, flow, VMA and VFA at that asphalt content all satisfy the medium-traffic criteria.

1. Back-calculate the effective specific gravity of the aggregate. The effective specific gravity is the one that treats the aggregate as though its surface-connected pores had already been filled by binder, and it follows from the single measured maximum specific gravity: $$G_{se}=\frac{100-P_b}{\dfrac{100}{G_{mm}}-\dfrac{P_b}{G_b}}=\frac{100-5.0}{\dfrac{100}{2.470}-\dfrac{5.0}{1.031}}=\frac{95}{40.486-4.850}$$ $$\boxed{G_{se}=2.666}$$
2. Check the absorbed asphalt implied by that result. The absorbed asphalt content follows from the difference between the effective and the bulk specific gravity of the aggregate: $$P_{ba}=100\,\frac{G_{se}-G_{sb}}{G_{sb}\,G_{se}}\,G_b=100\,\frac{2.666-2.696}{(2.696)(2.666)}(1.031)=-0.43\ \text{per cent}$$ The effective specific gravity has come out below the bulk specific gravity, which is physically impossible — an aggregate cannot absorb a negative amount of binder. The data as printed are therefore mildly inconsistent, and the correct engineering response is to set P_ba = 0, take the effective asphalt content equal to the total asphalt content, and continue: the three volumetric quantities that decide the design are formed from G_mb, G_mm and G_sb directly, so none of them is affected. The consequence is recorded as an assumption below.
3. Compute the theoretical maximum specific gravity at every trial asphalt content. With G_se fixed, the maximum specific gravity of the void-free mixture at any asphalt content is $$G_{mm}=\frac{100}{\dfrac{100-P_b}{G_{se}}+\dfrac{P_b}{G_b}}$$ Evaluating at 4.0 per cent asphalt gives 100/(96/2.666 + 4/1.031) = 2.5068, and the same substitution at the remaining trial points gives 2.4883, 2.4700, 2.4520 and 2.4342. The value at 5.0 per cent reproduces the measured 2.470 exactly, which confirms that the back-calculation in step 1 is arithmetically sound.
4. Compute the air voids at every trial asphalt content. The air voids are the shortfall of the compacted bulk specific gravity below the void-free value: $$VTM=100\left(1-\frac{G_{mb}}{G_{mm}}\right)$$ At 4.0 per cent asphalt, 100(1 − 2.360/2.5068) = 5.86 per cent; repeating at each trial point gives 4.43, 3.04, 1.92 and 0.79 per cent. Air voids fall steeply and almost linearly as binder replaces air in the skeleton.
5. Compute the voids in the mineral aggregate and the voids filled with asphalt. The VMA is obtained from the aggregate fraction alone and the VFA from the two previous results: $$VMA=100-\frac{G_{mb}\,P_s}{G_{sb}},\qquad P_s=100-P_b\qquad\text{and}\qquad VFA=100\,\frac{VMA-VTM}{VMA}$$ At 4.0 per cent asphalt VMA = 100 − (2.360)(96)/2.696 = 15.96 per cent and VFA = 100(15.96 − 5.86)/15.96 = 63.31 per cent. Carrying this through all five trials produces the complete volumetric table.

   Volumetric analysis of the five Marshall trial mixes

   Pb, %	Gmb	Gmm	VTM, %	VMA, %	VFA, %	Stability, kN	Flow, 0.25 mm
   4.0	2.360	2.5068	5.86	15.96	63.31	6.3	9
   4.5	2.378	2.4883	4.43	15.76	71.89	6.7	10
   5.0	2.395	2.4700	3.04	15.61	80.54	5.4	12
   5.5	2.405	2.4520	1.92	15.70	87.79	5.1	15
   6.0	2.415	2.4342	0.79	15.80	95.00	4.7	22

   The VMA curve passes through a minimum of 15.61 per cent at about 5.0 per cent asphalt and rises on either side, which is the classic shape and confirms that the trial series brackets the design point.
6. Plot the design curves and read the asphalt content at 4 per cent air voids. The Asphalt Institute procedure fixes the design asphalt content from the air-void criterion and then uses the remaining curves as checks.
   Figure 4.1 — The six Marshall design curves. Shaded bands are the Asphalt Institute medium-traffic acceptance ranges; the vertical dashed line is the design asphalt content of 4.65 per cent read from the 4 per cent air-void criterion.
   Interpolating the air-void curve between the 4.5 and 5.0 per cent trials, $$P_{b,design}=4.5+\left(\frac{4.43-4.00}{4.43-3.04}\right)(0.5)$$ $$\boxed{P_{b,design}=4.66\approx 4.7\ \text{per cent by mass of mix}}$$
7. Read the remaining properties at the design asphalt content and check them against the criteria. Interpolating each curve at 4.65 per cent asphalt gives VMA = 15.7 per cent, VFA = 74.6 per cent, stability 6.3 kN and flow 10.6 units of 0.25 mm. The Asphalt Institute medium-traffic criteria and the 9.5 mm minimum VMA at 4 per cent design voids require a stability of at least 5.34 kN, a flow between 8 and 18, a VMA of at least 15.0 per cent and a VFA between 65 and 78 per cent. Every one of these is satisfied: $$6.3>5.34\ \text{kN};\quad 8\le 10.6\le 18;\quad 15.7>15.0\ \text{per cent};\quad 65\le 74.6\le 78\ \text{per cent}$$ $$\boxed{\text{Design asphalt content}=4.7\ \text{per cent; all medium-traffic criteria satisfied}}$$ The margins are not equal, and it is worth saying which one is tight: the VMA clears its minimum by only 0.7 percentage points and the VFA sits 3.4 points below its upper bound, so a small increase in asphalt content would push the VFA out of range before anything else failed. That asymmetry is why the design content is quoted at the air-void value rather than at the peak of the stability curve, which lies at 4.5 per cent and would leave the mix marginally too dry.