I have got a ton of rocks and broken concrete in my soil. Trying to turn an problem into an asset, I have placed them around on top of my sheet mulches and hugelkultures. In our high desert climate, the extra heat will be very useful. Also, the snow here tends to evaporate from the surface, without melting into the soil. This is a big problem, since most of our precipitation comes in the form of snow. I am hoping that the heat from the rocks and south hugel faces will melt the snow.
I am wondering what would be the best way to darken the pieces of concrete, helping them absorb more energy. Would charcoal rubbed onto a damp stone stay very long? I know that charcoal is spread onto snowy fields in Tibet to hasten the spring thaw and warm the soil. Or does color make that much difference in this case? (Concrete and asphalt both seem to get pretty hot, despite color differences. )
Search out some of the threads on biochar. If your biochar were spread once spring temperatures are within a few degrees of thawing the snow, you will hasten the melt and prevent sublimation. In the fall, gather up a ton of dusty soil to mix with the char. A small percentage will blacken it. Darkness of the material makes a huge difference in sun absorption. This is more noticeable at lower temperatures. You noted that both concrete and asphalt get hot in the summer sun. Check out what happens on a sunny morning after the cool of night. The dark material heats faster. Later in the day, both materials are hot and radiating heat to the surrounding environment and may seem to have the same absorption qualities but they don't.
I was wondering about a combination of these ideas. Come spring, I will mix together a natural paint of sorts, containing biochar, fish oil, fish emulsion, possibly a little manure, and some crumbled up lichens and moss. The biochar will act as a black pigment and also absorb the other ingredients; the lichen will colonize the rock; the fish oil will keep everything stuck on till the lichen can grow; the fish emulsion will add nutrients to speed lichen growth; and the manure will add water absorption and some more nutrients. Now, the only question is, which lichens can grow on alkaline rocks and concrete in hot sun in a dry climate, even with the added help of my "paint" and some watering?
I know there are some, since lichens grow in the Negev. I will just have to hunt around I suppose. If I mixed pond water and fungi into the mix, would they naturally associate into lichens?
Get a cheap bag of cement mix, mix it up on the thin side (closer to mortar consictancy), add finely powdered charcoal dust ("Carbon Black") to darken, paint on a thin layer of this onto the surface of your rocks/concrete chunks. Congratulations: you have less toxic and long term blackened rocks.