where to dispose of dirt, concrete, asphalt or anything similar

Years ago I had this problem. I put pieces of concrete into garbage cans, adding a bit more each time.

One day I could hear the garbage truck really straining to lift the can... then somebody was pounding like crazy on my door...

I didn't answer it but even tho there was no prohibition against throwing away chunks of concrete, a nearly full can might be an issue.

Asphalt can be more difficult to get rid of due to environmental restrictions.