This is an ant in south-eastern Australia, but it might not be native.
I have found information on ants with one or more of the below
features attributed to their species, but none which has all of them:

*Black
*Large for a 'small ant' (maybe 3mm)
*Very strong formic acid smell when crushed
*Associated with branch and whole-tree failures (ie, when the tree or
branch comes down, these ants and their smell are there), especially
in candlebarks
*Currently in 'excavating' a fairly young (maybe 20 years) eucalypt
(narrow-leaf peppermint) that I would not have thought had rotten
wood.
*Producing a lot of 'sawdust' at base of tree.

(I know that the CSIRO has an identification site, but not having the
equipment - or the desire - to do things like measure ant hair length
or count ant teeth, it is no use to me)

What about sending the CSIRO one (two, three, dead uncrushed, your
problem), maybe packed in a little hole in piece of cardboard so so
that it/they don't get flattened in the post.  Maybe it is variety of
termite.

you can have it identified if you are willing to pay for it........

http://www.sardi.sa.gov.au/pages/entomolo/ent_diag02.html:sectID=3&tempID=2