OpenSpecEngineering

Proportions one cubic meter of normal-weight concrete by the ACI 211.1 absolute volume method [1], [2]. It gives the cement, water, coarse aggregate and fine aggregate batch masses for a first trial batch. Pick the aggregate size, slump, exposure, strength and sand fineness, and the page takes the mixing water, air content, water–cement ratio and coarse-aggregate volume from the ACI 211.1 tables. Each pick also has a Custom option to type your own value.

Equations

C = W/(w/c)     CA = (b/b₀)·γ_DR

V_FA = 1 − W/1000 − C/(1000·G_c) − A/100 − CA/(1000·G_CA)     FA = V_FA·1000·G_FA

W is the mixing water and C the cement, in kg/m³. w/c is the water–cement ratio by mass. b/b₀ is the dry-rodded volume of coarse aggregate per unit volume of concrete, and γ_DR its dry-rodded unit weight. A is the air content in percent. G_c, G_CA and G_FA are the specific gravities of the cement and of the saturated surface-dry (SSD) coarse and fine aggregate. CA and FA are the aggregate masses. The fine aggregate fills whatever volume is left, V_FA [1].

Limits and common mistakes

• The strength is the required average strength f′_cr, not the specified f′_c. f′_cr is higher, by a margin set from the plant’s test record [2].
• The table w/c is for strength only. A durability limit for freezing, sulfates or chlorides can call for a lower w/c, so use the smaller of the two.
• The tables are only for normal-weight aggregate up to 150 mm and 28-day strengths of 15–40 MPa. Air-entrained concrete has no 40 MPa row.
• The masses are SSD. Adjust the water and aggregate for the actual moisture of the stockpiles before batching, then correct the mix from the trial batch’s slump, yield and air.

Worked example

A driveway slab exposed to freeze–thaw needs air-entrained concrete with a 75–100 mm slump and an average strength of 30 MPa. The stone is 25 mm crushed rock with a dry-rodded unit weight of 1,600 kg/m³ and SSD specific gravity 2.68. The sand has a fineness modulus of 2.60 and specific gravity 2.64.

1. Choose Nominal Maximum Aggregate Size 25 mm (1 in.) and Concrete Air-entrained.
2. Choose Slump 75–100 mm (3–4 in.) and Air Content Air-entrained — moderate exposure.
3. Choose Required Average Strength 30 MPa and Fine-Aggregate Fineness Modulus 2.60.
4. Enter Dry-Rodded Unit Weight 1600, Specific Gravity — Cement 3.15, Coarse Agg. 2.68 and Fine Agg. 2.64, and press Solve. The Solution shows: Cement: 388.889 kg/m³
   Water: 175 kg/m³
   Coarse aggregate (SSD): 1,104 kg/m³
   Fine aggregate (SSD): 645.752 kg/m³
   Fine aggregate volume fraction: 0.244603
   Total batch mass: 2,313.64 kg/m³
   Water–cement ratio (check): 0.45
   Air content used: 4.5 %
   Coarse-aggregate bulk volume b/b0 used: 0.69
   From ACI 211.1 tables: water, air, w/c, b/b0

Check by hand: the volumes are water 0.175, cement 388.9/3150 = 0.1235, air 0.045 and stone 1104/2680 = 0.4119 m³. They leave 1 − 0.7554 = 0.2446 m³ of sand, or 0.2446 × 2640 = 645.8 kg. A total near 2,300 kg/m³ is typical for air-entrained normal-weight concrete.