At times of no fight the ring is empty. Excavation continues. Roads leading to the ring also lead from the ring, taking excess material to the citys outskirts (at first by truck and then conveyer as the ring becomes more established and excavation continuous). The boxing ring is located on top of excavator, the arm of which provides the only route to the boxing ring. When there is a fight the city empties and the ring fills. Excavation stops (?)
At the moment I envisage the excavation arm to be like a huge vertical spinning lathe, maybe needs to span whole way across, though I quite like if it stops at the boxing ring.