16-Civ-B7 Transportation Planning and Engineering · December 2015

Question 8 of 8: Marshall Mixture Volumetrics and Asphalt Cement Grading

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

Question 8: Marshall Mixture Volumetrics and Asphalt Cement Grading (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 — volumetric properties of the mixture

Given. The aggregate blend and the Marshall specimen data printed with the question.

Find. The air-void content $V_a$, the voids in the mineral aggregate VMA, the percentage of binder absorbed $P_{ba}$ and the effective binder content $P_{be}$.

Approach. Combine the individual aggregate gravities into blend values by the harmonic (volumetric) rule, obtain the bulk specific gravity of the compacted specimen from its saturated surface-dry and submerged masses and the theoretical maximum gravity from the effective blend gravity, and then apply the standard volumetric identities.

1. Blend specific gravities. Gravities combine by volume, so the blend value is the reciprocal of the mass-weighted sum of reciprocals: $$G_{sb} = \frac{100}{\frac{55}{2.370}+\frac{15}{2.390}+\frac{30}{2.390}} = \frac{100}{42.035} = \boxed{2.379}$$ $$G_{se} = \frac{100}{\frac{55}{2.390}+\frac{15}{2.410}+\frac{30}{2.410}} = \frac{100}{41.685} = \boxed{2.399}$$ The mineral filler is present at 0 % and drops out; that it is listed at all is a reminder to check the proportions sum to 100 %, which they do.
2. Bulk specific gravity of the compacted specimen. Only the saturated surface-dry mass and the submerged mass are supplied, so $$G_{mb} = \frac{A}{B-C} = \frac{1375.0}{1375.0-745.0} = \frac{1375.0}{630.0} = \boxed{2.183}$$
3. Theoretical maximum specific gravity. With $P_s = 100 - P_b = 96.25\ \%$ of aggregate by mass, $$G_{mm} = \frac{100}{\frac{P_s}{G_{se}}+\frac{P_b}{G_b}} = \frac{100}{\frac{96.25}{2.399}+\frac{3.75}{1.010}} = \frac{100}{43.835} = \boxed{2.281}$$
4. Air voids. The air-void content is the shortfall of the compacted gravity below the void-free gravity: $$V_a = 100\,\frac{G_{mm}-G_{mb}}{G_{mm}} = 100\,\frac{2.281-2.183}{2.281} = \boxed{4.33\ \%}$$
5. Voids in the mineral aggregate. VMA is the volume not occupied by the aggregate's own bulk volume: $$VMA = 100 - \frac{G_{mb}P_s}{G_{sb}} = 100 - \frac{2.183(96.25)}{2.379} = 100 - 88.30 = \boxed{11.70\ \%}$$
6. Absorbed binder. The difference between the effective and bulk aggregate gravities measures the pore volume the binder has entered: $$P_{ba} = 100\,\frac{G_{se}-G_{sb}}{G_{sb}G_{se}}\,G_b = 100\,\frac{2.399-2.379}{2.379(2.399)}(1.010) = \boxed{0.354\ \%}$$ expressed as a percentage of the aggregate mass.
7. Effective binder. What remains coats the particles and controls durability: $$P_{be} = P_b - \frac{P_{ba}}{100}P_s = 3.75 - 0.00354(96.25) = \boxed{3.41\ \%}$$ As a check, the voids filled with asphalt are $VFA = 100(VMA-V_a)/VMA = 100(11.70-4.33)/11.70 = 63.0\ \%$, and the volumetric identity $VMA = V_a + V_{be}$ closes with $V_{be} = P_{be}G_{mb}/G_b = 7.37\ \%$.
8. Read the numbers as a mix designer would. The air-void content of 4.3 % is squarely inside the 3–5 % design window, and the voids filled with asphalt at 63 % sit just below the 65–75 % band for heavy traffic. The VMA, however, is 11.70 % against a minimum of about 14 % for a 12.5 mm nominal maximum size — a serious deficiency. A mixture with too little VMA cannot hold enough effective binder to be durable no matter what binder content is chosen: at 3.41 % effective asphalt the films are thin, and the pavement will ravel and age prematurely. The correct recommendation is not to add binder, which would drive the air voids below 3 % and invite flushing, but to change the gradation — the blend is 45 % sand and fines and almost certainly too close to the maximum-density line — so that the aggregate skeleton opens up and VMA rises above 14 %.

Part B — classifying and grading asphalt cements in Canada

Three grading systems have been used on Canadian projects, and the question's example labels conflate two of them: AC-10 is a viscosity grade, while PG 64-22 is a performance grade, not a penetration grade. The penetration system labels its products differently, as 85/100 or 150/200. Setting the labels straight is the first thing a grader looks for, because the three systems measure genuinely different things.

Penetration grading is the oldest of the three. A standard needle loaded with 100 g is allowed to penetrate a sample held at 25 °C for five seconds, and the depth of penetration in tenths of a millimetre is the grade: a 150/200 asphalt admits the needle between 15.0 and 20.0 mm, and is therefore softer than an 85/100. The supporting tests are the ring-and-ball softening point, ductility at 25 °C, flash point, solubility in trichloroethylene, and the thin-film oven test with penetration measured again on the residue to represent ageing during mixing. The label is easy to interpret — a bigger number means a softer binder — and the test is cheap and quick. Its weaknesses are that penetration is an empirical index with no units of engineering meaning, that it is measured at only one temperature, and that two binders with the same penetration can behave very differently at the temperature extremes that matter in Canada.

Viscosity grading replaced penetration in an attempt to make the measurement fundamental. The grade is set by the absolute viscosity at 60 °C, measured in a capillary viscometer under vacuum and expressed in poises: AC-10 denotes 1000 ± 200 poises at 60 °C, and AC-20 twice that. Kinematic viscosity at 135 °C in a capillary viscometer supports the high-temperature mixing and compaction requirements, and the specification also carries penetration at 25 °C, flash point, ductility and solubility. The AR series applies the same idea to the aged residue rather than to the tank binder. Viscosity grading gives a property with real units at a temperature representative of hot summer pavement, and it grades stiffness monotonically, which penetration does not. It is still a two-temperature system, however, and it says nothing about cracking in a prairie winter.

Performance grading came out of the Strategic Highway Research Program and is now the basis of Canadian specifications through AASHTO M320, with the multiple-stress creep recovery specification M332 increasingly used alongside it. The label PG 58-34 states the two pavement design temperatures the binder is certified for: the average seven-day maximum pavement temperature, 58 °C, and the minimum pavement design temperature, −34 °C. The tests follow the binder through its life. The dynamic shear rheometer measures the rutting parameter $G^{*}/\sin\delta$ on the original binder and on residue from the rolling thin-film oven test, so that rutting resistance is checked when the pavement is new and after construction ageing. The pressure ageing vessel simulates five to ten years of oxidation, after which the dynamic shear rheometer measures the fatigue parameter $G^{*}\sin\delta$ at an intermediate temperature, and the bending beam rheometer measures the creep stiffness and the $m$-value at low temperature. Where the binder is brittle, the direct tension test supplies the failure strain. The rotational viscometer confirms that the binder can be pumped and mixed at 135 °C.

In the Canadian context the performance-graded system is decisively better, and for a reason that is specific to this country: the low-temperature grade is selected from the actual design air temperature at the site, so a binder specified for Winnipeg (PG 58-34) is not the same product as one specified for Vancouver (PG 58-22), even though both must resist the same summer rutting. Neither the penetration nor the viscosity system contains any low-temperature criterion at all, and thermal cracking is the dominant distress over most of Canada. Performance grading also grades the binder in the condition it will be in when the distress occurs — aged — and it accommodates polymer-modified binders, which the older empirical systems misrepresent because their consistency measurements are not sensitive to elastic recovery. The costs are real: the equipment is expensive, the tests take longer, and a small supplier cannot certify a wide range of grades economically, so the grade "bumping" that agencies apply for slow or heavy traffic has to be specified explicitly. The MSCR test in M332 addresses the last of these by measuring non-recoverable creep compliance and percent recovery directly, which characterises modified binders better than $G^{*}/\sin\delta$ alone and is replacing grade bumping in several provincial specifications.

The practical position is that penetration grading survives only in legacy specifications and in some emulsion and cutback work, viscosity grading is largely historical in Canada, and performance grading is what a designer should specify today — naming the reliability level and the traffic-adjusted grade explicitly, and checking the selected low-temperature grade against the site's design air temperature rather than against a provincial default.