Concrete mix design

A concrete mix design chooses the proportions of cement, supplementary materials, water, fine and coarse aggregate, air and admixtures so that the concrete is workable when fresh, strong and durable when hardened, and as economical and low-carbon as possible. The designer starts from the specification, which sets the strength, the exposure class, the maximum aggregate size and the slump, and works through a sequence of choices, each based on a well-established relationship. The result is a recipe for one cubic meter (or cubic yard) that is then checked by trial batches.

For the interchange deck, the state specification calls for a specified compressive strength of 5000 psi at 28 days, exposure categories F3 and C2 under ACI 318 (exposed to freezing and thawing with de-icing salts, and to external chlorides), 3/4 in nominal maximum aggregate, a slump of 3 ± 1 in at the point of discharge, and air content of 5 to 8 percent. Tamarack reviews the supplier's submitted mix and checks it with trial batches.

The goals of mix design

Every mix balances competing goals. More water makes concrete easier to place but weaker and more permeable. More cement raises strength but adds cost, heat, shrinkage and carbon. Larger aggregate reduces paste demand but cannot fit between closely spaced reinforcement. Air entrainment protects against frost but each percent of air lowers strength by roughly 5 percent. A good designer meets every requirement with the least paste and the lowest practical water content.

Specifications increasingly allow performance-based requirements, where the producer chooses the proportions freely as long as tested properties (strength, chloride penetration resistance, shrinkage) meet stated limits, instead of prescriptive limits on cement content and water–cement ratio. Most work, however, still combines a few prescriptive durability limits with a specified strength.

Step 1: the required average strength

As lesson 1 explained, test results scatter, so the mix must average more than the specified strength. Acceptance rules in both Canadian and US practice say, in essence, that the average of any three consecutive strength tests must equal or exceed the specified strength, and that no single test may fall more than a set amount below it (3.5 MPa, or 500 psi, for ordinary strengths). Requiring that each criterion be failed no more than about once in a hundred times leads to the familiar formulas for the required average strength when the producer has a reliable standard deviation \(s\):

These are the ACI 318 formulas for specified strengths up to 5000 psi (in customary units the second term is \(f'_c + 2.33s - 500\ \text{psi}\)). The constants come from the normal distribution: 1.34 is 2.33 divided by the square root of 3, because an average of three tests has a standard deviation \(s/\sqrt{3}\). When no standard deviation is available, larger fixed margins (for example 1200 psi for strengths of 3000 to 5000 psi) apply until enough data are gathered.

Step 2: the water–cementitious materials ratio

The water–cementitious materials ratio (w/cm) is the mass of water divided by the total mass of cement plus SCMs. It is chosen as the smaller of two values: the ratio needed for strength, read from the producer's own strength versus w/cm curve or from published tables, and the maximum ratio allowed for durability by the exposure class.

ACI 318 assigns exposure categories F (freezing and thawing), S (sulfate), W (water contact) and C (corrosion protection), each with classes 0 to 3, and sets a maximum w/cm, a minimum specified strength and air content for each. Classes F3 and C2, typical for bridge decks with de-icing salts, carry a maximum w/cm of 0.40 and a minimum strength of 5000 psi; state DOTs often specify additional limits.

The w/cm needed for strength depends on the materials. Each producer develops its own curve from trial batches, because cement brand, SCM type and aggregate change the relationship. Air-entrained concrete needs a lower w/cm than non-air-entrained concrete for the same strength.

Step 3: water content and air

The water needed for a given slump depends mainly on the maximum aggregate size and shape and on the air content. Larger and rounder aggregate needs less water. Published tables (such as those in ACI 211.1, the widely used guide for proportioning normal-weight concrete) give typical water contents; for 20 mm (3/4 in) crushed aggregate, air-entrained concrete at 75 to 100 mm (3 to 4 in) slump needs roughly 180 kg/m³ (305 lb/yd³) before admixtures. A normal-range water reducer cuts this by 5 to 10 percent and a high-range one by 12 to 30 percent.

The air content target comes from the exposure class and the aggregate size: smaller aggregate means more paste and therefore more air is needed to protect the paste. For 20 mm aggregate and severe exposure, a target of about 6 to 6.5 percent is common, within a specified range such as 5 to 8 percent.

Step 4: cementitious materials content

The mass of cementitious materials follows from the water content and the w/cm. The designer then splits it between cement and SCMs according to the specification and the exposure. Some specifications also set a minimum cementitious materials content, though modern practice discourages unnecessarily high cement contents because they add heat, shrinkage and carbon without improving durability.

Step 5: coarse aggregate content

The volume of coarse aggregate per unit volume of concrete is read from a table based on the nominal maximum size of the coarse aggregate and the fineness modulus of the sand: coarser sand and larger coarse aggregate allow more coarse aggregate. For 20 mm aggregate and a sand with FM 2.80, a typical value is 0.62 cubic meters of dry-rodded coarse aggregate per cubic meter of concrete. Multiplying by the dry-rodded bulk density gives the oven-dry mass.

Step 6: fine aggregate by absolute volume

Everything else in the cubic meter is sand. The absolute volume of each ingredient is its mass divided by its density (relative density times the density of water). The sand volume is whatever is left after subtracting the volumes of water, cementitious materials, air and coarse aggregate from one cubic meter.

Finally, the masses are converted to batch masses by correcting for the aggregates' moisture, as in lesson 2, and admixture doses are set from manufacturers' recommendations and trial batches.

Lucie programs the absolute volume method so that Tamarack can quickly check suppliers' submittals and see how changing one choice, such as the air content or SCM blend, affects the rest of the mix.

def absolute_volume_mix(water, wcm, blend, air, ca_factor, ca_rodded, g_ca, g_fa):
    """Returns oven-dry masses (kg per m3) by the absolute volume method."""
    cm = water / wcm
    masses = {name: frac * cm for name, (frac, g) in blend.items()}
    vol = water / 1000 + air
    vol += sum(masses[n] / (g * 1000) for n, (frac, g) in blend.items())
    ca = ca_factor * ca_rodded
    vol += ca / (g_ca * 1000)
    fa = (1 - vol) * g_fa * 1000
    return {"water": water, **masses, "coarse": ca, "fine": fa}

blend = {"GUL": (0.70, 3.15), "slag": (0.25, 2.90), "silica fume": (0.05, 2.20)}
for air in (0.055, 0.065, 0.075):
    mix = absolute_volume_mix(160, 0.38, blend, air, 0.62, 1650, 2.68, 2.62)
    density = sum(mix.values())
    parts = ", ".join(f"{k} {v:.0f}" for k, v in mix.items())
    print(f"air {100*air:.1f} %: {parts}; density {density:.0f} kg/m3")

air 5.5 %: water 160, GUL 295, slag 105, silica fume 21, coarse 1023, fine 691; density 2295 kg/m3
air 6.5 %: water 160, GUL 295, slag 105, silica fume 21, coarse 1023, fine 665; density 2269 kg/m3
air 7.5 %: water 160, GUL 295, slag 105, silica fume 21, coarse 1023, fine 639; density 2243 kg/m3

Raising the air from 5.5 to 7.5 percent removes about 50 kg of sand from each cubic meter and lowers the density. It also lowers the strength, which is why the producer controls air content closely and why the field technician measures it on every acceptance sample.

Trial batches and adjustments

Calculated proportions are a starting point. The mix is checked in the laboratory or plant by trial batches that measure slump, air content, density (to check the yield) and strength at several ages. If the slump is low, water reducer is adjusted rather than water, so the w/cm stays fixed. If the yield is off, meaning a batch intended to make one cubic meter makes noticeably more or less, the aggregate masses are corrected. For important projects, trial batches also test durability properties such as rapid chloride permeability or bulk resistivity, freeze–thaw resistance and shrinkage.

Reviewing a submitted mix design

On most projects the engineer does not design the mix; the ready-mix supplier submits one, and the engineer or testing firm reviews it. Amara's checklist is short. Does the w/cm meet the exposure limit, calculated with all cementitious materials and all water, including water in admixtures and free water on aggregates? Is the air content target inside the specified range? Are the SCM proportions allowed for the exposure and the season? Is there field data, from at least fifteen to thirty tests on a similar mix, showing the producer's standard deviation and that the mix has met the required average strength? Do the stated volumes add up to one cubic meter? Are the aggregates from approved sources with current test reports, including alkali reactivity? A submission that cannot answer these questions goes back for revision before the first truck is ordered, because problems are far cheaper to fix on paper than in a deck.

Special concretes

• High-performance concrete for decks and marine structures uses low w/cm (0.35 to 0.40), silica fume or slag, and high-range water reducers to reach very low permeability.
• Self-consolidating concrete flows into forms without vibration. It uses more fine material, a high-range water reducer and often a viscosity-modifying admixture, and it is tested by slump flow rather than slump.
• Mass concrete uses low-heat cements and high SCM contents, larger aggregate and sometimes cooling pipes to control temperature.
• Lightweight concrete uses expanded shale, clay or slate aggregate to reduce dead load, at densities of about 1600 to 1900 kg/m³ (100 to 120 lb/ft³).
• Fiber-reinforced concrete adds steel, synthetic or glass fibers to control cracking or replace some reinforcement in slabs on grade and shotcrete.