South Carolina's landfill bans do most of the work here. As Greenville County states on its own disposal services page, state law bans electronic waste, motor oil, yard waste, car batteries, appliances and tires from the landfill, and those items are collected and recycled separately instead.
Hazardous waste and liquid waste are refused as well, along with paint, solvents, fuel and asbestos in a standard container.
Twin Chimneys adds its own refusals in the construction area, and two of them catch people out. Any waste that has been in contact with petroleum products is unacceptable, and so is any waste that has been in contact with friable asbestos material. Lead-acid batteries, waste oil and yard or brush waste are also excluded from that part of the site.
What the landfill does take is broad: brick and masonry block, concrete, hardened cement and cured asphalt, lumber including treated lumber, plaster and plasterboard, shingles and roofing, insulation, carpet and vinyl flooring, tile, pipes, structural steel, vinyl siding, wall coverings, glass, mirrors, rock, topsoil and earthen material, stumps and large logs.
The City's own position is simple and it is why you need a container: building waste, rubble and cast-off material from construction, repair or demolition will not be hauled by the City unless arrangements are made and paid for through the public services office.
If something on your site does not clearly fit, check it with your account manager before it goes in.