Subtracts what is put back from what is dug out to give the spoil to be carted away. Excavated soil swells, so the volume to haul is the in-place volume multiplied by a swell factor, which is about 1.2 for ordinary soil.
Whatever is dug out and not used as backfill has to be carted away as spoil. This finds that volume and the number of loads.
is the swell factor, about 1.2 for ordinary soil and over 1.5 for rock.
Soil packed in the ground gains air between its grains once it is broken up, and takes more space than before. That increase is the swell factor. The undisturbed state is called in-place and the dug state loose. Trucks carry loose soil, so the volume to haul is not the in-place volume: at 1.2 it is a fifth more.
An excavation 10 m by 8 m and 1.5 m deep is 120 m³ in place. Putting 40 m³ back leaves 80 m³ of spoil, which at a swell factor of 1.2 is 96 m³ to haul. In 4 m³ trucks that is 24 loads.
A negative figure for spoil means the excavation cannot supply all the fill and soil has to be brought in. The material simply travels the other way; the arithmetic of the loads is the same.
Backfill is compacted, so it shrinks again. A precise takeoff applies a compaction factor as well; here the backfill volume is simply subtracted.