I would like to differentiate between a tunnel (i.e. the Channel Tunnel) and one of its 'sub'-tunnels. For example the Channel Tunnel is a 'tunnel complex' consisting of three 'sub'-tunnels - one service tunnel and two main tunnels. So, either a word for the complex (other than the name) or a word for a 'sub'-tunnel would do.
For instance, in Dutch there is the word 'tunnel' to describe the tunnel including all 'sub'-tunnels and the word 'tunnelbuis' to describe a single 'sub'-tunnel. 'Tunnelbuis' can literally be translated to 'tunneltube' or 'tunnelpipe'.
In the Wikipedia article of the Channel Tunnel there is mention of three 'bores'. However, this does not seem to be in widespread use or specifically for a tunnel created with a TBM.
The southern _____ of the tunnel is 30cm longer than the northern _____.