Question 5 of 5: Superpave volumetric mix design for three trial blends

Question 5: Superpave volumetric mix design for three trial blends (20 marks: a–e 3 each, f 5)

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.

Given. Five aggregate stockpiles proportioned three ways, one PG 58-28 binder, and two gyratory specimens per blend compacted to N_max with heights recorded at three gyration counts.

Find. (a) G_sb and G_sa per blend; (b) G_se and P_ba; (c) estimated and corrected G_mb at the three gyration levels; (d) G_mm; (e) %G_mm per specimen and blend average; (f) the remaining volumetrics and the selected blend.

Approach. Work down the standard volumetric chain: combine the stockpile specific gravities, estimate G_se and the absorbed binder, convert gyratory heights into estimated bulk specific gravities and correct them against the measured value, compute G_mm, express densification as %G_mm, and finally test each blend against the Superpave criteria for the design traffic level.

1. Fix the compaction effort from the design traffic. A design ESAL of 8,000,000 falls in the “3 to less than 30 million” band, for which the Superpave gyratory levels are $$N_{ini} = 8, \qquad N_{des} = 100, \qquad N_{max} = 160$$ and the acceptance criteria are $\%G_{mm}$ at $N_{ini} \le 89.0$, at $N_{des} = 96.0$ and at $N_{max} \le 98.0$. The nominal maximum aggregate size is 12.5 mm (the largest stockpile is a 1/2 in chip), so the minimum voids in the mineral aggregate is 14.0 % and the acceptable range of voids filled with asphalt is 65 to 75 %.
2. (a) Combine the stockpile specific gravities by the harmonic (volume-weighted) rule. The appendix gives $$G_{sb(\text{comb})} = \frac{100}{\dfrac{P_1}{G_{sb1}}+\dfrac{P_2}{G_{sb2}}+\cdots+\dfrac{P_n}{G_{sb(n)}}}$$ and the same form applies to $G_{sa}$. For Blend #1, for example, $$G_{sb} = \frac{100}{\dfrac{26}{2.701}+\dfrac{14}{2.688}+\dfrac{21}{2.723}+\dfrac{19}{2.695}+\dfrac{20}{2.677}} = \frac{100}{37.0716} = 2.698$$ Repeating for all three blends: $$\boxed{G_{sb} = 2.698,\ 2.696,\ 2.701} \qquad \boxed{G_{sa} = 2.766,\ 2.768,\ 2.767}$$ The three blends are almost indistinguishable on specific gravity, which is expected — the five stockpiles come from the same quarry and span only 0.046 in $G_{sb}$. The differences between the blends will therefore have to come from gradation and binder content, not from the aggregate itself.
3. (b) Estimate the effective specific gravity and the absorbed binder. $G_{se}$ cannot be back-calculated from $G_{mm}$ here, because $G_{mm}$ is itself asked for in part (d). It is instead estimated from the standard Asphalt Institute observation that asphalt fills about 80 % of the water-permeable pore volume: $$G_{se} \approx G_{sb} + 0.8\left(G_{sa}-G_{sb}\right)$$ For Blend #1, $G_{se} = 2.698 + 0.8(2.766-2.698) = 2.753$. The absorbed binder then follows from the appendix relation $$P_{ba} = 100\,\frac{G_{se}-G_{sb}}{G_{se}\,G_{sb}}\,G_{b} = 100 \times \frac{2.7525-2.6978}{2.7525 \times 2.6978} \times 1.03 = \boxed{0.759\ \%}$$ and the three blends give $$G_{se} = 2.753,\ 2.753,\ 2.753 \qquad P_{ba} = 0.759,\ 0.794,\ 0.729\ \%$$ Absorption below 1 % marks these as low-absorption aggregates, so the difference between total and effective binder will be small but not negligible.
4. (c) Turn the gyratory heights into estimated bulk specific gravities. During compaction the specimen is a 150 mm diameter cylinder, so its volume at any gyration count is $V = \tfrac{\pi}{4}(15.0\ \text{cm})^{2}\,h$, and the estimated bulk specific gravity is the dry mass divided by that volume. For Blend #1 specimen A at $N_{max}$, $h = 110.8\ \text{mm} = 11.08\ \text{cm}$: $$V = \frac{\pi}{4}(15.0)^{2}(11.08) = 1958.0\ \text{cm}^{3}, \qquad G_{mb,\text{est}} = \frac{4902.7}{1958.0} = 2.504$$ and at $N_{des}$ and $N_{ini}$ the same specimen gives 2.402 and 2.205.
5. Correct the estimates against the measured value at N_max. The estimate assumes a perfect cylinder and therefore always understates the density, because the specimen surface is rough and its true volume is smaller than the mould volume. The measured value uses the saturated-surface-dry method: $$G_{mb,\text{meas}} = \frac{A}{B-C} = \frac{4902.7}{4729.8-2809.0} = \frac{4902.7}{1920.8} = 2.552$$ so the correction factor for this specimen is $$C_{f} = \frac{G_{mb,\text{meas}}}{G_{mb,\text{est}}\big|_{N_{max}}} = \frac{2.5524}{2.5041} = \boxed{1.0194}$$ Multiplying every estimated value by that factor gives the corrected profile $$G_{mb}(N_{ini}) = 2.248, \quad G_{mb}(N_{des}) = 2.449, \quad G_{mb}(N_{max}) = 2.552$$ The six correction factors range from 1.0005 to 1.0210, all comfortably inside the 1.00–1.03 band that indicates a sound specimen.
6. (d) Compute the theoretical maximum specific gravity of each blend. With $G_{se}$ from step 4 and $P_s = 100-P_b$, $$G_{mm} = \frac{100}{\dfrac{P_s}{G_{se}}+\dfrac{P_b}{G_b}}$$ For Blend #1, $G_{mm} = 100/\left(95.4/2.7525 + 4.6/1.03\right) = 100/39.125 = 2.556$. The three blends give $$\boxed{G_{mm} = 2.556,\ 2.549,\ 2.525}$$ falling as the binder content rises, since binder is roughly 2.5 times lighter than the aggregate it displaces.
7. (e) Express the densification as a percentage of G_mm. $\%G_{mm} = 100\,G_{mb}/G_{mm}$ at each gyration level, averaged over the two specimens of each blend:

   Densification, %G_mm (blend averages)

   Blend	Nini (limit ≤ 89.0)	Ndes (target 96.0)	Nmax (limit ≤ 98.0)
   #1	88.16  ✓	95.95  ✓	99.85  ✗
   #2	86.02  ✓	96.03  ✓	97.09  ✓
   #3	88.13  ✓	95.98  ✓	97.85  ✓

   All three blends land essentially on the 96.0 % target at $N_{des}$, which is the check that the whole chain of assumptions is right — the binder contents were chosen to hit 4 % air voids, and they do. Blend #1 fails at $N_{max}$: at 99.85 % it is within 0.15 % of being void-free under refusal compaction, which is the classic signature of a tender mix that will rut and flush under traffic.
8. (f) Complete the volumetrics at N_des. Using the appendix relations with the corrected $G_{mb}$ at $N_{des}$, $$V_a = 100\,\frac{G_{mm}-G_{mb}}{G_{mm}}, \quad VMA = 100 - \frac{G_{mb}P_s}{G_{sb}}, \quad VFA = 100\,\frac{VMA-V_a}{VMA}, \quad P_{be} = P_b - \frac{P_{ba}P_s}{100}$$ which give

   Volumetric properties at N_des

   Blend	Gmb	Va (%)	VMA (%)	VFA (%)	Pbe (%)	DP
   #1	2.452	4.05	13.28  ✗	69.50	3.88	1.29  ✗
   #2	2.448	3.97	13.58  ✗	70.77	4.04	1.24  ✗
   #3	2.424	4.02	15.10  ✓	73.39	4.71	1.06  ✓

   The dust proportion is $DP = P_{0.075}/P_{be}$; the paper does not print the gradation, so a dust content of 5.0 % passing the 0.075 mm sieve is assumed (a typical value for a 12.5 mm Superpave mix) and the column is reported on that basis.
9. Select the mix. Every blend meets the 96.0 % target at $N_{des}$ and the 89.0 % limit at $N_{ini}$, so the decision turns on the two remaining screens. Blend #1 is eliminated twice over — it over-compacts at $N_{max}$ (99.85 % against a 98.0 % ceiling) and its VMA of 13.28 % is 0.7 points below the 14.0 % floor. Blend #2 survives the densification screens but fails VMA at 13.58 %. Only Blend #3 clears everything: 88.13 % at $N_{ini}$, 95.98 % at $N_{des}$, 97.85 % at $N_{max}$, VMA 15.10 %, VFA 73.39 % inside the 65–75 % band, and DP 1.06 inside 0.6–1.2. Therefore $$\boxed{\text{Select Blend \#3 at } P_b = 5.4\,\%}$$ The physical story behind the arithmetic is straightforward: Blend #3 carries the most 3/8 in chip and manufactured sand and the least coarse stone, which opens up the aggregate skeleton, raises VMA by nearly two points, and leaves room for the 4.71 % of effective binder that a durable surface course needs. Blends #1 and #2 are richer in coarse stone, pack too tightly, and cannot hold enough binder without losing their air voids.