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Use a concrete recycler to get rid of old concrete that you have had to remove. You can also try to find a use for the leftover concrete before it dries. See "eHow to Use Leftover Concrete."
How to Dispose of Leftover Concrete. It is very possible that you will have some concrete left over when you finish that masonry project. Disposing of it can be a problem or an added benefit. Let's look at some of the options available.
Get rid of leftovers delivered by a ready-mix company from a large job the easiest way of all. Simply have them take it with them. (You still pay for it, but the cost of paying and not using it is less than trying to get rid of a large amount on your own later.) Larger ready-mix companies have machines called 'reclaimers' that separate out the concrete mix while it is still wet so that the sand and coarse aggregate can be used again.
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Check your phone book under 'Concrete Recycling.' These companies make money breaking up hardened concrete and selling it to be reused elsewhere. Allow the small amount of concrete you have left over to harden on grass or cardboard. (Make sure the pieces are small enough to be handled after they dry or you will be breaking them up with a sledgehammer.) This hardened concrete can then be hauled to the recycling plant.
Try your city or county dump as a last resort. Some take old concrete, but the cost is usually high. Using this disposal method, it often costs more to get rid of the old concrete than the new concrete costs.