【Dig】 , 【delve】 , 【spade】 , 【grub】 , 【excavate】 mean to use a 【spade】  or similar utensil in breaking up the ground to a point below the surface and in turning or removing the earth or bringing to the surface of something below it.

【Dig】 , the commonest word, implies a loosening of the earth around or under something so as to bring it to the surface, or a disturbing of the earth by such loosening.

【Dig】 may imply also a result comparable to that obtained by spading or a bringing to the surface or out of concealment or prolonged laborious effort as in study or research.

【Delve】 implies the use of a 【spade】 or more often of efforts comparable to the use of a 【spade】 and carries a stronger connotation of laboriousness and depth of penetration (as in the work of a gardener or of one who cultivates an interest).

【Spade】 is often interchangeable with 【dig】 but even more frequently than the latter is applied to a turning of the earth in manual (as opposed to mechanical) preparation of soil for planting.

【Grub】 may denote a digging and turning of soil but more often implies a clearing of soil by digging out something (as roots, stumps, and stones); often it suggests the hard, dirty, exhausting nature of such work and with this feeling may be used of various tasks, labors, or duties.

In some cases 【grub】  reflects the disorder of the land-clearing process and denotes a haphazard and laborious rummaging.

【Excavate】  suggests making a hollow in or through something (as the ground, a mass of rock, or a mountainside) by or as if by means of a 【spade】 or shovel or a machine which performs the operations of spading and shoveling.