I used to work for a couple of cities. This is likely a utility trench,
and the utility should have an open encroachment permit with the city
that requires adequate compaction and pavement over any trenches. All
you should have to do is to call the City Engineer and tell him/her of
the inadequate compaction and pavement.
Make sure to note the time and date of the phone call in case nothing
happens and you need to escalate the issue to the Public Works Director.
Bob Shanteau