New Zealand government gave three criteria for the definition of  ‘essential’ construction. One is  "Any entity involved in building and construction related to essential services and critical infrastructure".

Therefore I believe tunnelling will go on. When I called a friend last week he confirmed that the work continued but this is in early stages yet, maybe later they stopped I don't know.

https://www.khl.com/international-construction/new-zealand-stops-all-but-essential-construction/143139.article