Mix Design of Concrete and Asphalt

NCEES FE Civil spec: Materials, A. Mix design of concrete and asphalt. FE Reference Handbook: Materials Science/Structure of Matter chapter (concrete) and Civil Engineering chapter (asphalt).

Mix design is the process of choosing proportions of binder, water, aggregate and air so a mixture meets strength, durability and workability targets. For concrete the FE Civil exam focuses on the water-cement ratio and the absolute volume method. For asphalt it focuses on volumetric properties: air voids, voids in mineral aggregate (VMA) and voids filled with asphalt (VFA).

What the NCEES spec covers

Section A, "Mix design of concrete and asphalt", asks you to compute batch quantities, apply moisture corrections to aggregates, interpret the water-cement ratio, and calculate the volumetric properties used to select an asphalt binder content (Marshall or Superpave style).

Key concepts

Water-cement ratio (w/c) by mass is the main control on concrete strength and permeability. Lower w/c means higher strength, as long as the mix can still be placed and consolidated.
Absolute volume method. The volumes of water, cement, aggregates and air in 1 m³ (or 1 yd³ = 27 ft³) must add up to that unit volume. Each solid volume is its mass divided by (specific gravity × density of water).
Aggregate moisture. Mix designs assume saturated surface-dry (SSD) aggregates. Wetter stockpiles add free water to the mix, so batch water is reduced and aggregate mass increased; drier aggregates do the opposite.
Air entrainment improves freeze-thaw durability but lowers strength by a few percent per percent of air.
Asphalt volumetrics. Gmb is the bulk specific gravity of the compacted mix, Gmm the theoretical maximum (no air), and Gsb the bulk specific gravity of the aggregate. Typical design targets are about 4% air voids, a minimum VMA that depends on aggregate size, and VFA in roughly the 65% to 75% range.

Core formulas

\frac{w}{c} = \frac{mass of water}{mass of cement} V_{i} = \frac{m _{i}}{S G _{i} ρ _{w}} \sum V_{i} + V_{air} = 1 m^{3}

V_{a} = 100 (1 - \frac{G _{mb}}{G _{mm}}) V M A = 100 - \frac{G _{mb} P _{s}}{G _{s b}} V F A = 100 \frac{V M A - V _{a}}{V M A}

Here $P_{s}$ is the aggregate content in percent of total mix mass.

Where it is in the FE Reference Handbook

The Materials Science/Structure of Matter chapter has concrete charts showing how compressive strength varies with water-cement ratio and age. Asphalt mix and pavement material relationships are in the transportation part of the Civil Engineering chapter; search the PDF for "VMA" to find them. The absolute volume bookkeeping itself is not spelled out, so practice it.

Worked example

A concrete mix per cubic meter uses 180 kg of water at w/c = 0.45, 1,050 kg of SSD coarse aggregate (SG 2.70) and 5% entrained air. Cement SG is 3.15 and the fine aggregate SG is 2.65. Find the cement content and the SSD mass of fine aggregate.

Step 1: cement.

c = \frac{180}{0.45} = 400 kg

Step 2: absolute volumes.

Ingredient	Calculation	Volume (m³)
Water	180 / 1,000	0.1800
Cement	400 / (3.15 × 1,000)	0.1270
Coarse aggregate	1,050 / (2.70 × 1,000)	0.3889
Air	0.05 × 1	0.0500
Subtotal		0.7459

Step 3: fine aggregate fills the rest.

V_{f a} = 1 - 0.7459 = 0.2541 m^{3} m_{f a} = 0.2541 (2.65) (1, 000) = 673 kg (SSD)

Asphalt check. A compacted specimen has Gmb = 2.345, Gmm = 2.448, Gsb = 2.680 and 95% aggregate by mass:

V_{a} = 100 (1 - \frac{2.345}{2.448}) = 4.2% V M A = 100 - \frac{2.345 ( 95 )}{2.680} = 16.9% V F A = 100 \frac{16.9 - 4.2}{16.9} = 75%

Common mistakes

Forgetting the air volume, which makes the fine aggregate mass too large.
Using oven-dry aggregate masses in an SSD-based design without a moisture correction.
Correcting for total moisture instead of moisture above absorption (free water).
Mixing up Gmb, Gmm and Gsb in the asphalt formulas.
Treating w/c by volume. It is always by mass.

Practice Problems

Try these from the free PolyCalc FE Civil problem bank. Each one has a full worked solution.

A concrete mix uses 180 kg of water and 360 kg of cement. What is its water-cement ratio by mass? See the worked solution or practice the Construction Materials deck
A concrete mix uses 350 kg of cement per cubic metre at a water-cement ratio of 0.45 by mass. The mixing water required is most nearly: See the worked solution or practice the Construction Materials deck
A batch calls for 1,000 kg of coarse aggregate in the saturated surface-dry condition. The aggregate has an absorption of 2% and arrives at a total moisture content of 4%. The free water carried into the mix by this aggregate is most nearly: See the worked solution or practice the Construction Materials deck
An asphalt mixture has Gmm = 2.50 and Gmb = 2.375. Its percent air voids is most nearly: See the worked solution or practice the Construction Materials deck
An asphalt mix has Gmb = 2.35, aggregate bulk specific gravity Gsb = 2.65 and aggregate content Ps = 95%. Its VMA is most nearly: See the worked solution or practice the Construction Materials deck
A mixture has VMA = 14% and air voids = 4%. The voids filled with asphalt (VFA) is most nearly: See the worked solution or practice the Construction Materials deck

Related Calculators and Examples

Frequently Asked Questions

What is the water-cement ratio?

It is the mass of mixing water divided by the mass of cement. It is the main control on concrete strength and durability: lower ratios give stronger, less permeable concrete.

How does the absolute volume method work?

Convert the mass of each ingredient to a solid volume using its specific gravity, add the air volume, and make the total equal one unit volume. The last ingredient, usually fine aggregate, fills the remaining volume.

What are typical air voids in an asphalt mix design?

Most dense-graded designs target about 4 percent air voids at the design compaction level, with minimum VMA and a VFA range that depend on the aggregate size and traffic.

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