16-Civ-B7 Transportation Planning and Engineering · May 2013

Question 2 of 7: Asphalt Mixture Volumetrics

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

Paper format. 98-Civ-B7 Highway Engineering, National Examinations May 2013 — a three-hour open-book examination; any non-communicating calculator is permitted. The cover page states that a total of five solutions is required, that only the first five as they appear in the answer book will be marked, and that all questions are of equal value. The grading scheme on the last page confirms 20 marks per question: Q1 (a) and (b) 10 marks each; Q2 (a) through (e) 4 marks each; Q3 (a) to (j) 2 marks each; Q4 (a) and (b) 10 marks each; Q5 (a) and (b) 10 marks each; Q6 (a) through (e) 4 marks each; Q7 20 marks. All seven printed questions are worked here, because this set is a study resource rather than a timed attempt; on exam day a candidate submits only the first five, in order. The paper also states that any data not given but required may be assumed, and that assumptions should be recorded with the answer — several questions below need that licence, and each assumption is flagged where it is made.

Reference texts. N.J. Garber and L.A. Hoel, Traffic and Highway Engineering, 5th ed. (geometric design, sight distance, vertical curves, earthwork, pavement design); AASHTO, Guide for Design of Pavement Structures (1993) (rigid and flexible thickness design, reliability, drainage and load-transfer coefficients); Transportation Association of Canada, Geometric Design Guide for Canadian Roads (Canadian design-domain values for sight distance and vertical curvature); Asphalt Institute, Mix Design Methods MS-2, 7th ed. (mixture volumetrics, VMA, VFA, absorbed binder); B.M. Das, Principles of Geotechnical Engineering, 9th ed. (compaction, Proctor testing, zero-air-voids line, CBR); M.S. Mamlouk and J.P. Zaniewski, Materials for Civil and Construction Engineers, 4th ed. (concrete and asphalt materials); A.M. Neville, Properties of Concrete, 5th ed., and CSA A23.1 (air entrainment, curing, joints in concrete pavement).

Check — assumptions carried through this paper. Three items are not supplied by the exam and are assumed under the paper’s own Note 2 (“any data, not given but required, can be assumed”), each stated again at the point of use: (i) Question 5 gives the mass of the Proctor mould but not its volume, so the ASTM D698 / AASHTO T99 standard 101.6 mm mould volume of 944 cm³ is used; (ii) Question 6 does not name a design speed, so the available stopping sight distance is computed from the Canadian/AASHTO eye and object heights of 1.08 m and 0.60 m; (iii) Question 7 lists the modulus of subgrade reaction as “1.0 MPa”, which is dimensionally incomplete — it is read as 1.0 MPa/m and the sensitivity of the answer to that reading is reported with the result.

Question 2: Asphalt Mixture Volumetrics (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.

Given. A compacted, laboratory-moulded asphalt concrete specimen whose bulk relative density and the three component relative densities have all been measured, with the binder content expressed on the total-mix basis.

Given data
Symbol	Quantity	Value
G_mb	Bulk specific gravity of the compacted mixture	2.329
G_b	Specific gravity of the asphalt binder	1.017
P_b	Binder content, percent by weight of total mix	6.0 %
G_se	Effective specific gravity of the aggregate	2.730
G_sb	Bulk specific gravity of the aggregate	2.715
P_s	Aggregate content = 100 − P_b	94.0 %

Find. The binder content on the aggregate-weight basis, the theoretical maximum specific gravity, the voids in the mineral aggregate, the percentage of those voids filled with binder, and the percentage of binder absorbed into the aggregate pores.

Figure 2.1 — Volumetric composition of the compacted specimen on a 100 % total-volume basis. VMA is everything above the aggregate bulk solid; VFA is the effective-binder share of it.

Approach. Work in a 100 g basis of total mix, so every percentage is directly a mass; the two different aggregate specific gravities (bulk and effective) are the whole point of the question, because their difference is exactly the pore volume into which binder is absorbed.

(a) Binder by weight of aggregate. Converting from the total-mix basis to the aggregate basis simply changes the denominator from 100 to $P_s=94$: $$P_{b,\text{agg}}=\frac{P_b}{100-P_b}\times 100=\frac{6.0}{94.0}\times 100 =\boxed{6.38\ \%\ \text{by weight of aggregate}}$$ This is the number a plant operator sets on the binder pump, and it is always the larger of the two.
(b) Maximum specific gravity of the mix. With zero air voids, the mixture volume is the effective aggregate volume plus the binder volume, so $$G_{mm}=\frac{100}{\dfrac{P_s}{G_{se}}+\dfrac{P_b}{G_b}} =\frac{100}{\dfrac{94.0}{2.730}+\dfrac{6.0}{1.017}} =\frac{100}{34.432+5.900}$$ $$G_{mm}=\frac{100}{40.332}=\boxed{2.479}$$ The effective gravity is the right one here because the binder cannot enter the aggregate pores that are already sealed by absorbed binder.
(c) Voids in the mineral aggregate. VMA is the volume of the compacted specimen not occupied by the aggregate bulk solid, expressed as a percentage of the total volume: $$\text{VMA}=100-\frac{G_{mb}\,P_s}{G_{sb}}=100-\frac{2.329\times 94.0}{2.715} =100-80.64=\boxed{19.36\ \%}$$ Note that the bulk gravity is used here, so that any binder absorbed into the aggregate is counted as part of the aggregate rather than as void space.
(d) Air voids, needed before voids filled with asphalt. The air voids are the shortfall of the compacted density below the void-free density: $$V_a=100\,\frac{G_{mm}-G_{mb}}{G_{mm}}=100\times\frac{2.479-2.329}{2.479}=6.07\ \%$$ Substituting into the definition of VFA, which is the fraction of the VMA occupied by effective binder, $$\text{VFA}=\frac{\text{VMA}-V_a}{\text{VMA}}\times 100 =\frac{19.36-6.07}{19.36}\times 100=\boxed{68.7\ \%}$$ The VMA and the VFA both sit inside the usual Marshall design windows for a heavy-duty surface course (VMA above about 14 % and VFA between 65 % and 75 %, widening to 65–78 % for medium traffic), but the air voids do not: 6.07 % is above the 3–5 % targeted at design, so this specimen is under-compacted rather than badly proportioned — the mineral skeleton and the binder are in the right ratio and it is compactive effort, not the job-mix formula, that is short.
(e) Absorbed binder. The volume of aggregate pore accessible to binder is the difference between the bulk and effective gravities; converting that volume to a mass of binder gives $$P_{ba}=100\,\frac{G_{se}-G_{sb}}{G_{sb}\,G_{se}}\,G_b =100\times\frac{2.730-2.715}{2.715\times 2.730}\times 1.017$$ $$P_{ba}=100\times\frac{0.015}{7.412}\times 1.017=\boxed{0.206\ \%\ \text{by weight of aggregate}}$$ The effective binder content that remains available to coat and bind the particles is therefore $$P_{be}=P_b-\frac{P_{ba}P_s}{100}=6.00-\frac{0.206\times 94.0}{100}=5.81\ \%$$ so this aggregate is barely absorptive and only about 3 % of the binder is lost into the stone.

Read as a set, the five answers tell a consistent story about one specimen: nearly all of the 6 % binder stays on the outside of the particles, it fills a little over two-thirds of the mineral skeleton’s voids, and the 6.1 % of air left over is what a roller in the field would still be expected to close up. Had the aggregate been a porous slag or a lightweight material, P_ba would have run to 1–2 % and the effective binder would have dropped far enough to leave a dry, ravelling surface at the same job-mix formula.

Quantity	Value
(a) Binder by weight of aggregate	6.38 %
(b) Maximum specific gravity, G_mm	2.479
(c) Voids in mineral aggregate, VMA	19.36 %
Air voids, V_a (intermediate)	6.07 %
(d) Voids filled with asphalt, VFA	68.7 %
(e) Absorbed binder, P_ba	0.206 % by weight of aggregate
Effective binder content, P_be	5.81 % by weight of total mix

Concept & Theory

Topic: Volumetric analysis of a compacted hot-mix asphalt specimen.

Key relations: G_mm = 100 / (P_s/G_se + P_b/G_b); V_a = 100(G_mm−G_mb)/G_mm; VMA = 100 − G_mbP_s/G_sb; VFA = 100(VMA−V_a)/VMA; P_ba = 100 G_b(G_se−G_sb)/(G_sbG_se); P_be = P_b − P_baP_s/100.

Why this works: Every one of these formulas is a volume balance on a 100 g sample. Mass divided by relative density is volume, so P_s/G and P_b/G are the aggregate and binder volumes; whether the aggregate volume is computed with G_sb or G_se decides whether the absorbed binder is counted inside the stone or outside it, and that single choice generates the whole family of quantities. VMA uses the bulk gravity because the mineral skeleton, pores and all, is what the binder and air must share the remaining space with; G_mm uses the effective gravity because absorbed binder is no longer free to occupy mixture volume.

Common pitfall: Interchanging G_sb and G_se. Using G_se in the VMA expression makes VMA look about 0.4 percentage points smaller and can push an otherwise acceptable mix below the specification limit; using G_sb in G_mm understates the maximum density and inflates the apparent air voids. A second trap is quoting P_ba on the total-mix basis: it is defined on the aggregate basis, exactly like the answer to part (a).

Source: Asphalt Institute, Mix Design Methods for Asphalt (MS-2), 7th ed., Ch. 3 (volumetric properties); M.S. Mamlouk and J.P. Zaniewski, Materials for Civil and Construction Engineers, 4th ed., Ch. 9.

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