Tonnes, cubic metres, brass and cubic feet: converting aggregate quantities

The BOQ pays for granular sub-base in cubic metres, finished in position. The crusher bills in tonnes. The local yard quotes per brass and the tipper owner talks in cubic feet. Somebody has to turn each of these into the others, and the wrong conversions are usually found at month end.

The volume conversions are fixed: 1 brass is 100 cubic feet, which is 2.83 cubic metres. Volume to weight is not fixed. It needs a bulk density, and for loose crushed aggregate that is typically somewhere between 1.50 and 1.75 tonnes per cubic metre. One brass of loose aggregate is therefore roughly 4.2 to 5 tonnes, and the only way to narrow that range is to weigh a load.

The four units

Why volume to weight has no single answer

Bulk density is the weight of a cubic metre of material as it lies, air gaps included. The rock may be the same from load to load. The gaps are not. No Indian standard fixes a bulk density for any of these materials, and four things move it.

• Size and grading. Single-size chips leave open voids. In a graded mix the small particles sit in the gaps between the large ones, so GSB and WMM weigh more per cubic metre than 20mm from the same rock.
• Rock type. Dense basalt and lighter sandstone crushed to the same size do not weigh the same.
• Moisture. Water adds weight to every material. Damp fines also bulk, taking up more volume for the same dry weight, so wet dust misleads in both directions. IS 2386 Part 3 is the test code for bulk density, voids, absorption and bulking.
• Placement. Stone dropped from a loader bucket is at its loosest. After a long haul it has settled, and under a roller it is a different material altogether.

Bulk densities you can start from

Compacted layers are a separate question. MoRTH Clauses 401 and 406 ask for GSB and WMM to be compacted to at least 98% of the maximum dry density from the heavy compaction test, IS 2720 Part 8. That maximum dry density is on the lab report for your material, and it is the figure for turning compacted cubic metres into tonnes. As a cross-check, a rate analysis reproduced from the MoRTH Standard Data Book works WMM at 2.2 tonnes per compacted cubic metre.

Rate analyses of the same kind typically allow about 1.28 cubic metres of loose material for each compacted cubic metre of GSB and about 1.32 for WMM, and some municipal analyses use 1.40. Treat those as planning factors that a trial stretch confirms. How much GSB and WMM a kilometre of road needs carries that calculation through.

Worked conversions

1. Brass to cubic metres: 6 brass x 2.832 = 16.99 m3.
2. Cubic metres to tonnes: 16.99 m3 of loose 20mm x 1.53 t/m3 = 26.0 tonnes.
3. Tonnes per brass: 2.832 m3 x 1.53 t/m3 = 4.33 tonnes of loose 20mm.
4. Tonnes to brass: a 30 tonne order of 20mm at 1.53 t/m3 is 30 ÷ 1.53 = 19.61 m3, and 19.61 ÷ 2.832 = 6.92 brass.
5. Cubic feet to tonnes: 1,000 cft ÷ 35.315 = 28.32 m3. At 1.53 t/m3 that is 43.3 tonnes, or about 43 kg per cubic foot.
6. Compacted WMM to tonnes: 225 m3 compacted at 2.2 t/m3 = 495 tonnes.

Why the weighbridge tonne ends the argument

Weight is not perfect. A wet load carries water that somebody pays for. But a tonne is one number read off a calibrated instrument, on a slip that travels with the load, and it can be checked on any other bridge. A volume is a tape measure, an opinion about how level the load was and a density nobody agreed.

This is why our aggregate supply is priced per tonne. There is a calibrated weighbridge at every plant, ten across our operations. Dispatch weight is the billed weight, and the slip goes with the tipper. Weighbridge slips and month-end reconciliation covers the slip itself.

Checking a load billed by volume

Sometimes the seller only deals in brass. Then the job is to find your own density and hold him to it.

1. Measure the inside of the tipper body: length, width and the depth of the load once it has been struck level. Not the height of the heap.
2. Multiply for the volume. A levelled load 4.0 m long, 2.2 m wide and 1.0 m deep is 8.8 m3, and 8.8 ÷ 2.832 = 3.11 brass.
3. Send three or four loads of each material over a weighbridge and divide the net weight by the measured volume. That is the loose bulk density for that material, from that source, in that season.
4. Use that density to turn every later challan into tonnes. Repeat the weighing when the source, the size or the weather changes.

Agree in the order where the volume is measured. A load settles on the haul, so a body that left the yard full can arrive looking short without having lost a kilogram. The weight also has to be legal: what a tipper may carry sets the ceiling whichever unit the load was sold in.