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 (9 marks). A compacted asphalt concrete specimen consists of three phases: aggregate, asphalt binder and air. The three quantities asked for divide the total volume between those phases, and every one of them is a percentage of the total compacted volume except VFA, which is a percentage of the aggregate voids.

(i) Air voids, VTM (voids in the total mix) are the small pockets of air distributed among the coated aggregate particles, expressed as a percentage of the bulk volume of the compacted specimen. They are obtained by comparing the bulk specific gravity of the compacted specimen with the theoretical maximum (void-free) specific gravity of the same mix, $VTM = 100(G_{mm} - G_{mb})/G_{mm}$. Air voids are the single most important volumetric property: too high (above about 8 %) and the mix is permeable to air and water, so the binder oxidises and the mix ravels and strips; too low (below about 3 %) and there is no room for the binder to expand into in hot weather, so the mix flushes and ruts. Design is therefore set at 4 %, with the expectation that traffic will densify the pavement to about 4 % in service from a higher as-constructed value.

(ii) Voids in the mineral aggregate, VMA, is the total volume of the intergranular void space between the aggregate particles in the compacted mix — that is, the air voids plus the volume of the effective (non-absorbed) asphalt — expressed as a percentage of the total volume. It is computed from the bulk specific gravity of the aggregate, $VMA = 100 - G_{mb}P_s/G_{sb}$, where $P_s$ is the aggregate content by mass. VMA is the space available to hold binder, so a minimum VMA is specified (15.0 % for a 9.5 mm nominal maximum size at 4 % design air voids, decreasing with increasing aggregate size). If VMA is too low the mix cannot carry enough binder to be durable without losing its air voids; if it is far too high the mix will lack aggregate interlock and stability. VMA is controlled almost entirely by aggregate gradation and particle shape, which is why a change in the aggregate source forces a redesign.

(iii) Voids filled with asphalt, VFA, is the percentage of the intergranular void space (VMA) that is occupied by the effective asphalt binder, $VFA = 100(VMA - VTM)/VMA$. It is a restatement of the same information in a form that is sensitive to durability: for a given VMA, VFA rises as the binder film thickens. The Asphalt Institute limits VFA to 65 to 78 % for medium traffic (70 to 80 % for light traffic, 65 to 75 % for heavy traffic). A low VFA means thin binder films, rapid ageing and cracking; a high VFA means the aggregate skeleton is close to being floated apart by binder, with rutting and bleeding to follow. VFA is the criterion that most often trims the acceptable asphalt-content window from above.

Part (b) — determining the design asphalt content (11 marks).

Given.

Find. The design asphalt content that gives 4 % air voids, and confirmation that the mix at that asphalt content satisfies every Asphalt Institute criterion for medium traffic.

Approach. Back-calculate the effective specific gravity of the aggregate from the single measured maximum specific gravity, use it to predict the maximum specific gravity at every trial asphalt content, then compute VTM, VMA and VFA for each trial mix, interpolate the asphalt content at 4 % air voids, and check stability, flow, VMA and VFA at that content.

1. Back-calculate the effective specific gravity of the aggregate. The maximum specific gravity was measured at only one asphalt content, so $G_{se}$ — the specific gravity of the aggregate including the pores that the asphalt does not penetrate — must be recovered from it: $$G_{se} = \frac{100 - P_b}{\dfrac{100}{G_{mm}} - \dfrac{P_b}{G_b}} = \frac{100 - 5.0}{\dfrac{100}{2.470} - \dfrac{5.0}{1.031}} = \boxed{2.6658}.$$ This one number lets the maximum specific gravity be predicted at every other asphalt content, which is what makes a single $G_{mm}$ measurement sufficient.
2. Check the absorbed asphalt and flag the data. Absorbed asphalt follows from the difference between the effective and bulk aggregate gravities, $$P_{ba} = 100\,\frac{G_{se} - G_{sb}}{G_{sb}\,G_{se}}\,G_b = 100\,\frac{2.6658 - 2.696}{2.696 \times 2.6658}(1.031) = -0.43\ \%.$$ The result is negative, which is physically impossible: it says the effective gravity of the aggregate is lower than its bulk gravity, whereas $G_{se}$ must always lie between $G_{sb}$ and the apparent gravity. The printed $G_{sb}$, $G_{mm}$ and $G_b$ are therefore not mutually consistent. The correct engineering response is to take $\boxed{P_{ba} = 0\ \%}$, so that the effective asphalt content equals the total asphalt content, $P_{be} = P_b$, and to proceed — VTM, VMA and VFA are computed from $G_{mb}$, $G_{mm}$ and $G_{sb}$ directly and are unaffected by this inconsistency.
3. Predict the maximum specific gravity at each trial asphalt content. With $G_{se}$ fixed, $$G_{mm} = \frac{100}{\dfrac{100 - P_b}{G_{se}} + \dfrac{P_b}{G_b}}.$$ At $P_b = 4.0\ \%$ this gives $100/[(96.0/2.6658) + (4.0/1.031)] = 2.5068$, and repeating at each content gives 2.5068, 2.4883, 2.4700, 2.4520, 2.4342. The value at 5.0 % reproduces the measured 2.470 exactly, which confirms the back-calculation.
4. Compute VTM, VMA and VFA for each trial mix. Using $VTM = 100(1 - G_{mb}/G_{mm})$, $VMA = 100 - G_{mb}(100-P_b)/G_{sb}$ and $VFA = 100(VMA - VTM)/VMA$, the volumetric summary is:

   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

   Air voids fall steadily with asphalt content, as they must, while VMA passes through a minimum near 5.0 %% asphalt — the classic shape, and a useful check that the arithmetic is sound.
5. Interpolate the asphalt content at 4 % air voids. The design air-void content of 4 % falls between the 4.5 % trial (VTM = 4.43 %) and the 5.0 % trial (VTM = 3.04 %). Linear interpolation gives $$P_b = 4.5 + (4.00 - 4.43)\,\frac{5.0 - 4.5}{3.04 - 4.43} = 4.655\ \%,$$ so the design asphalt content is $\boxed{P_b = 4.65\ \%}$ — say 4.7 % — by mass of total mix. Figure 4.1 shows the construction.
6. Read the other properties at the design asphalt content and check every criterion. Interpolating each curve at $P_b = 4.65\ \%$ gives VMA = 15.7 %, VFA = 74.6 %, corrected stability = 6.3 kN and flow = 10.6 units of 0.25 mm (that is 2.65 mm). The Asphalt Institute criteria for medium traffic, with the VMA minimum taken from the 9.5 mm nominal maximum size at 4 % design air voids, are compared below.

   Property at design Pb	Value	Asphalt Institute criterion (medium traffic)	Verdict
   Air voids, VTM	4.0 %	3 to 5 %	Satisfied (by construction)
   Voids in mineral aggregate, VMA	15.7 %	15.0 % minimum (9.5 mm NMPS)	Satisfied
   Voids filled with asphalt, VFA	74.6 %	65 to 78 %	Satisfied
   Marshall stability	6.3 kN	5.34 kN (1,200 lb) minimum	Satisfied
   Marshall flow	10.6 (0.25 mm)	8 to 18 units of 0.25 mm	Satisfied

   Every criterion is met, so the design is accepted at that asphalt content. It is worth noting that VMA clears its minimum by only 0.7 percentage points, so this mix has very little reserve: a small coarsening of the aggregate gradation in production would push VMA below 15 % and the mix would have to be redesigned.

Final results.