Our dogs tunnel near the fence because my neighbor has dogs and they
want to talk to each other. :-)

I haven't done anything yet, but for me, barbed wire it out of the
question. I've been thinking about laying some sort of bricks or
railroad ties along the side of the fence. It seems like if I do that
in certain areas, they just relocated and dig elsewhere. So, I might
just do it all along the fence and see what happens...