You have to activate BC nodes as the tunnel advances, which can be set up using a "modulation function". To do add such a function, in the data panel, right-click (for example) "hydraulic-head bc", select "add parameter" and then select "modulation function". This will add an editable variable beneath hydraulic had bc that you can set up just like any other nodal variables.
Another approach would be to used transient material properties, simulating the advancing tunnel by increasing the K. You would still have a BC at the tunnel entrance to simulate discharge from it.
Pete