Concrete Mix and Quantities: Method

Absolute Volume, Quantities, Maturity and Evaporation

Scope

The first dropdown chooses one of three calculations: the proportions of a trial mix, the quantities of a job, or the maturity of placed concrete with the evaporation rate at its surface. The mix calculation follows chapter III of the Bureau of Reclamation Concrete Manual (8th edition, 1975) and reproduces its Example 1 with the default inputs. The tool carries the manual's Table 14 (air, sand and water by maximum aggregate size) and Table 16 (strength against water-cement ratio), which are the Bureau's own. It carries no table of ACI 211.1, ACI 318 or any other copyrighted document: where a specification or code sets a value (the durability limit on the ratio, the minimum cementitious content, exposure air contents) the value is an input. A computed mix is a first trial. Every source the tool uses says the same thing: the proportions are confirmed and adjusted by trial batches made with the job materials.

Units

The specified strength, the standard deviation, densities, the batch volume, the bag weight, all lengths, the truck and bag volumes, the mesh weight and the wind speed go through the unit menu and convert with the unit switch. Contents of the mix are plain numbers read as lb/yd³ in US customary units and kg/m³ in SI, and prices are per ton or tonne, per cubic yard or cubic metre, per pound or kilogram and per square foot or square metre in the same way; the unit switch does not convert these, so re-enter them after switching. A water content, air content, sand percentage or dry-rodded volume left blank is taken from Table 14 and converted. The maturity analysis has its own temperature unit, and the temperature-time factor is always in °C·h (1 °C·h = 1.8 °F·h).

Required average strength

Strength tests scatter, so the mix is aimed above the specified strength f′_c. Four choices are offered.

Coefficient of variation (Concrete Manual, section 62): f′_cr = f′_c / (1 − t V), with V the coefficient of variation of the tests and t = 0.703, 0.883 or 1.100 for 75, 80 or 85 percent of the tests above f′_c. The Bureau designs for 80 percent and takes 15 percent as average control, which gives 3,460 lb/in² for a 3,000 lb/in² design strength. The equation reproduces all 135 entries of the manual's Table 21 within the 10 lb/in² they are rounded to.

Standard deviation: the larger of f′_c + 1.34 s and f′_c + 2.33 s − 500 lb/in², the rule of ACI 301 and of earlier editions of ACI 318 as the Unified Facilities Guide Specification 03 70 00 prints it (the first expression for s up to 505 lb/in², the second above). The first expression guards the average of consecutive tests, the second guards against a single test far below f′_c. For a specified strength above 5,000 lb/in² the second expression is 0.90 f′_c + 2.33 s. A record of fewer than 30 tests multiplies s by the entered factor (1.16 for 15 tests, 1.08 for 20).

No test record: f′_c + 1,000 lb/in² below 3,000, f′_c + 1,200 from 3,000 to 5,000, and 1.1 f′_c + 700 above 5,000 lb/in², as printed in the same guide specification.

None: the specified strength is used as it is, as Army Field Manual 5-428 does in its example.

Water-cementitious ratio

The ratio for strength is entered, or read from Table 16 of the Concrete Manual by straight-line interpolation at f′_cr (0.564 for 3,458 lb/in², which the manual rounds to 0.56). The table gives probable minimum average strengths of air-entrained concrete, with and without a water-reducing admixture, for ratios of 0.40 to 0.70; the manual calls it conservative and intends it for the first trial only. The durability limit is entered. The lower of the two ratios is used, and the cementitious content is the water content divided by it, or the specified minimum content if that is larger.

Proportions by absolute volume

One unit volume of concrete (27 ft³ or 1 m³) is the sum of the solid volumes of its ingredients and the air. The solid (absolute) volume of an ingredient is its weight divided by its specific gravity times the density of water; the air is its percentage of the unit volume. Water, cement, pozzolan and slag are fixed by the steps above, so the aggregate volume is what remains. It is divided in one of two ways.

Percent sand: the sand is the entered (or Table 14) percentage of the total aggregate by solid volume and the coarse aggregate is the rest. This is the method of the manual's examples.

Dry-rodded coarse aggregate: the weight of coarse aggregate is the entered (or Table 14) percentage of the unit volume times its dry-rodded unit weight, and the sand fills the remaining volume. The Concrete Manual and FM 5-428 use that weight directly as the batch weight; when the unit weight was measured on oven-dry aggregate, the second option multiplies it by one plus the absorption to reach the saturated surface-dry weight.

The manual's printed weights come from volumes rounded to 0.01 ft³. The tool does not round intermediate values, so its coarse aggregate in Example 1 is 2,133 lb where the manual prints 2,134 lb and the total is 3,946 lb against 3,947 lb. In Example 2 the manual prints 107 lb of pozzolan for 353 × 0.30 = 106 lb.

The indices table gives the cement factor in bags, the unit weight (total weight over unit volume), the air-free unit weight, and the paste, mortar and coarse aggregate shares of the volume.

Batch weights and moisture

Proportions are for saturated surface-dry (SSD) aggregate. Stockpiled aggregate with total moisture M and absorption A, both in percent of oven-dry weight, is weighed at SSD weight × (1 + M) / (1 + A). The difference from the SSD weight is free water when positive, and is taken off the water added at the mixer; when negative it is water the aggregate will absorb, and is added. With the absorption set to zero the moisture entered is the free moisture on the SSD weight, which is how both manuals state their examples (sand 5 percent, coarse aggregate 1 percent in the default). The batch is sized by volume or by whole bags of cement.

Admixture doses per 100 lb or 100 kg of cementitious material are multiplied out per unit volume and per batch. The dose by percent follows the manual: millilitres = cementitious weight × percent / 100 × grams per unit weight / (grams of the dosed substance per millilitre of product). Water in the admixtures is not deducted from the mixing water.

A unit weight measured on the fresh trial batch gives the yield (batch weight / unit weight), the relative yield, the air content by the gravimetric method (air-free unit weight less measured unit weight, over the air-free unit weight) and the contents actually obtained per unit volume.

Quantities

Each row of the table is a shape with a count. Slab and footing: A × B × C. Wall: A × B × (C + D)/2, with C the thickness at the top and D at the base. Rectangular column and beam: A × C × D. Round column or pier: π C²/4 × A. Curb: A × C × D. Stairs: width A times the section of the flight, which is the steps (rise C × run D / 2 each) on a waist slab of the entered thickness measured square to the soffit, steps × (C D/2 + waist × √(C² + D²)). The form contact area counted for each shape is listed in the results table; it leaves out bulkheads, wall ends and anything cast against earth.

The net volume is increased by the waste allowance. For ready-mixed concrete it is rounded up to the ordering increment and divided by the truck capacity; for bagged mix it is divided by the yield of one bag and rounded up. With the contents of a site-mixed concrete entered per unit volume, the cement (in whole bags), sand, coarse aggregate and water for the job follow. The default rows are the retaining wall of FM 5-428 (63.7 yd³). The manual rounds the volume before adding waste and so orders 495 sacks of cement where the unrounded figure is 494.

The reinforcing mat is a rectangle with bars each way. The number of bars in a direction is the width across them less twice the edge cover, divided by the spacing and rounded down, plus one; each run is the length less twice the cover. A run longer than the stock length is made of pieces lapped by the entered lap length, pieces = ⌈(run − lap) / (stock − lap)⌉, and each lap adds its length to the steel. Weights are the nominal weights of ASTM A615 bars, No. 3 to No. 18. Hooks, chairs, dowels and cutting waste are not included. Mesh is its area plus the lap allowance, times the entered weight per unit area.

Maturity

The temperature-time factor of Nurse and Saul is M = Σ (T − T₀) Δt, where T is the average concrete temperature of each interval between readings and T₀ the datum temperature, traditionally −10 °C. An interval colder than the datum adds nothing. The equivalent age of Freiesleben Hansen and Pedersen is t_e = Σ exp[−(E/R)(1/T − 1/T_r)] Δt with absolute temperatures, R = 8.314 J/(mol·K), the apparent activation energy E and the reference temperature T_r. NIST found E between 30,000 and 64,000 J/mol for different cementitious systems; near 30,000 J/mol the age factor is almost linear in temperature and the two functions agree, while near 60,000 J/mol the Nurse-Saul function is inaccurate. The optional factor B gives the simpler NIST function t_e = Σ exp[B (T − T_r)] Δt.

The strength-maturity relationship of the mixture is entered as points (index, strength) from cylinders cured beside a temperature record. The tool fits S = a + b log₁₀(index) by least squares, the usual form for the temperature-time factor, and also interpolates linearly between the points. For a target strength it inverts the fit and finds the age at which the history reaches that index, or how many more hours at the last recorded temperature are needed. The default history and curves are illustrations, not data of a real mixture. A maturity estimate holds only for the mixture the curve was made with, needs enough moisture for hydration, and does not see errors in batching or placing; ASTM C1074 gives the procedure and its checks.

Evaporation of bleed water

Plastic shrinkage cracks form when water evaporates from a fresh surface faster than bleeding replaces it. The rate is estimated with the equation behind the familiar nomograph, attributed to Menzel: W = 0.44 (e_o − e_a)(0.253 + 0.096 V) in lb/ft²/h, with e_o the saturation vapour pressure at the concrete temperature, e_a the vapour pressure of the air (saturation pressure at the air temperature times the relative humidity), both in lb/in², and V the wind speed in miles per hour. The Federal Highway Administration's curing guide prints it for spreadsheets as ER = 4.88 [0.1113 + 0.04224 WS/0.447] × 0.0443 [exp(0.0302 (1.8 CT + 32)) − (RH/100) exp(0.0302 (1.8 AT + 32))] in kg/m²/h, with WS in m/s and temperatures in °C; the tool uses this form. Uno's formula, E = 5 ([T_c + 18]^2.5 − r [T_a + 18]^2.5)(V + 4) × 10⁻⁶ kg/m²/h with V in km/h and r the relative humidity as a fraction, is printed beside it; the two differ by up to about 20 percent because they fit the vapour pressure differently.

The rate is compared with an entered limit. UFGS 03 30 00 requires precautions when the rate would exceed 1 kg/m²/h (0.2 lb/ft²/h), after ACI 305R. The FHWA guide points to 0.5 kg/m²/h as the start of hot-weather conditions and warns that paving concrete, which bleeds little, may be at risk above about 0.3 kg/m²/h. The result table gives the wind speed at which the limit is reached, and the chart shows the rate against wind speed.

Not covered

The Table 14 corrections for fineness modulus, slump and air content are stated in the tooltip of the aggregate-size field but are not applied automatically. Trial-batch adjustment, aggregate grading and blending, volumetric batching with sand bulking, lightweight and mass concrete, temperature of the fresh concrete, rebar schedules by bar mark, bends and hooks, and formwork design pressure are outside the tool.