I've used 4" and 6" PVC gutter downpipe as ventilation tube in small diameter tunnels before now. Works well and doesn't collapse if you lay on it, lean against it, put something on top of it or just switch the fan off for a while.
joints made from short sections of layflat plus jubilee clips, steel-fixers tie wire or denso tape.
of course handling sections into a cave isn't always easy, but you can cut it with a hacksaw or ripsaw. Would probably work well with the airco fan previously mentioned, with the major caveat that you DON'T want 240v anywhere out of doors. 110v will sting a bit of you get a belt from it but isn't dangerous, just unpleasant, whereas 240v can be fatal
''the stopes soared beyond the range of our caplamps' - David Bick...... How times change .... oh, I don't know, I've still got a lamp like that.