On private property, including your driveway or inside a fenced construction site, Saratoga Springs requires no container permit.
The licensing answer is clearer here than in most cities, and it is in your favor. The city makes it unlawful to haul or remove garbage or refuse without being the city, its agent, or an authorized hauler. The decisive point is how those two words are defined. Garbage means waste from preparing, handling, storing, cooking or consuming food. And refuse is defined as waste matter from occupying a dwelling or operating a business, with an express carve-out: refuse does not include industrial waste or waste matter resulting from the construction, demolition, or repair of a building or other structure.
So the city's prohibition reaches food waste and ordinary household and business waste, and the material a construction container is for sits outside both definitions. There is a separate route where a commercial establishment needs permission from the City Manager, but read its scope: that applies to commercial garbage, which is the food-waste definition again. It is not a route a construction container needs.
The city also sets no vehicle standard at all in its solid waste chapter. There is no requirement for an enclosed, watertight or compacting truck, which is not true in every Utah city, so a properly tarped open-top container on a tilt frame satisfies Saratoga Springs on the published words.
The city's rules on container type and on keeping containers closed are written about receptacles provided by the city or its agent for material the city collects, so they do not reach a private construction container. And the city's streets, business regulations and utilities titles between them never mention a container of our kind in more than three hundred thousand characters, in either direction. So treat a street or shoulder placement as a question for the City of Saratoga Springs before you book, and your account manager will get you the contact.
Statewide, Utah now requires a load going to a landfill to stay securely covered from its point of origin until it is tipped, and landfills collect a fine at the gate for an uncovered load. That duty sits on whoever is driving, which on a rental is us. If you are hauling anything yourself in a trailer, the same duty applies to you.