A lot of it depends on the time in Rome's history that you are describing. Roman Armies typically set up a castra or camp that they would would march out from. Often times preexisting physical structures like a river would serve as a latrine, with it being downstream from other uses the army might make of the river.

Most permanent camps would be fed from Rome's series of aqueducts.

The main character Attilius in Robert Harris' novel, Pompeii, is an aquarius or hydraulic engineer. His job is to inspect and maintain the water supply. This involves the sewers. There is some neat historical contextualisation of what that profession would have entailed. You might be interested in checking that out.