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"Cut and fill" refers to the practice of excavating soil to make a hole in the ground and then refilling it later. The extracted material tends to increase in volume as it is no longer subject to the in-situ stress or in other words, the soil that has been dug up gets bigger because it isn't being squashed any more by the weight of soil surrounding it.
This means that the volume of the hole or excavation will be smaller than the pile of material excavated and so you would have to squash (this process is more correctly described as consolidation and compaction) the soil to make it fit back into the original hole it came from.
Therefore the volume of the cut material (the hole) must be considered separately from the volume of the fill (the pile of earth or soil removed).
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