Concrete, aggregates, density and earthwork factors

Lesson 4 calculated the volumes of elements as they appear on the drawings. Those geometric volumes are only the start. Concrete arrives in trucks of limited size and must keep flowing at a steady rate; aggregates are bought by mass but placed and compacted by volume; and soil changes volume as soon as it is dug, swelling when it is loosened and shrinking when it is compacted. This lesson connects volume to mass through density, plans concrete deliveries and pour rates, converts between bank, loose and compacted earth, and explains why a contractor who ignores these factors can be badly wrong on trucking, disposal and fill costs even when every geometric volume is correct.

Density and unit weight

Density is mass per unit volume. It turns a volume into a mass, which is what trucks, cranes, scales and suppliers care about. In SI it is expressed in kilograms per cubic metre (kg/m³), or tonnes per cubic metre. In US customary units, unit weight is expressed in pounds per cubic foot (lb/ft³ or pcf), and aggregate suppliers often quote tons per cubic yard.

Because 1 m³ of water has a mass of 1,000 kg, densities in kg/m³ divided by 1,000 give the specific gravity, the ratio of a material's density to that of water. Normal concrete with a density of 2,400 kg/m³ has a specific gravity of 2.4. In US units, 150 lb/ft³ × 27 = 4,050 lb per cubic yard, a little over two short tons.

Ready-mixed concrete: trucks and pour rates

Ready-mixed concrete is delivered in truck mixers that typically carry a maximum of about 7 to 10 m³ (about 9 to 12 yd³), depending on the truck and on legal axle limits. Suppliers charge extra for short loads below a minimum, for waiting time beyond an allowance per load and for after-hours delivery. Planning a pour therefore involves the total volume, the size of each load, the rate at which the crew and pump can place concrete, and the travel time from the plant.

The interval between trucks should match the placing rate, so that a truck is ready as the previous one empties but none wait long enough for the concrete to stiffen or for waiting charges to start. Specifications limit the time from batching to discharge, commonly to about 90 to 120 minutes, and allow less in hot weather.

For small jobs, bagged concrete mix is common. Bag yields are printed on the bag and are typically about 0.014 m³ for a 30 kg bag and about 0.60 ft³ for an 80 lb bag. Dividing the required volume by the yield gives the number of bags; a fence post hole needing 0.05 m³ takes 0.05 ÷ 0.014 = 3.6, so 4 bags of 30 kg.

Mix proportions by mass

Modern concrete is batched by mass, not volume, because mass is easier to measure accurately. A mix design states the mass of each ingredient per cubic metre or cubic yard of concrete. The water–cement ratio, or water to cementing materials ratio when fly ash or slag replaces part of the cement, is the mass of water divided by the mass of cementing materials. Lower ratios give stronger, more durable concrete, and exposure classes in the standards set maximum ratios for concrete exposed to freezing, de-icing salts or sulphates.

Aggregates: bought by mass, placed by volume

Granular base, crushed stone and sand are usually bought and delivered by mass, but drawings specify them by compacted thickness. To order, calculate the compacted volume, multiply by the compacted density to get the mass, add a waste or overrun allowance and round up to whole truckloads. The compacted density comes from the supplier or from field density tests on similar work.

Bank, loose and compacted earth

Soil in the ground is in its natural or bank state. When it is excavated, the particles are loosened and air fills the spaces between them, so the same mass occupies more volume: the loose state. When it is placed and compacted, the particles are forced closer together, often closer than they were in the ground: the compacted state. Earthwork quantities must always state which state they refer to, usually as bank cubic metres (bank m³) or bank cubic yards (BCY), loose (LCY) and compacted (CCY).

• Swell is the percentage increase in volume from bank to loose: Loose volume = Bank volume × (1 + swell).
• Shrinkage is the percentage decrease in volume from bank to compacted: Compacted volume = Bank volume × (1 − shrinkage).
• The load factor converts loose volume back to bank volume: load factor = 1 ÷ (1 + swell).

Trucks haul loose material, so truck capacities are loose volumes. Disposal sites may charge by load, by mass or by volume. Fill requirements are compacted volumes, but borrow is bought or excavated in the bank state. Mixing the three states is one of the commonest and most expensive errors in earthwork estimates.

Whether excavated soil can be reused as backfill depends on its type and moisture and on the specification, which may require imported granular fill around foundations and under slabs. Contaminated soil requires testing and disposal at licensed facilities, at costs many times higher than clean fill. The arithmetic is the same; the unit prices are very different.

Moisture and bulking of sand

Moisture changes both mass and volume. Wet aggregate weighs more than dry, so a tonne of wet sand contains less sand than a tonne of dry sand, and concrete plants correct batch weights for measured moisture. Damp sand also bulks: a thin film of water holds particles apart, so damp sand can occupy 20 to 30 % more volume than the same sand dry or fully saturated. This is another reason why batching by volume is unreliable and why sand should be measured by mass where accuracy matters.