AC has a prooduct called terra wash that works pretty well on non organic stuff. I'm using on concrete at bank drive-throughs.

I use a product from Spray nine called Grez-Off that's great for oil and fat based stains and is biodegradable

Look for a butyl based product I think that terra wash is butyl based.

Russ from Southside has some truck cleaning detergents that should work well for soot/road grit.

Check out Brown Derby, I have seen it in action and it was literally amazing. It was taking zebra stripes off gutters, cleaning vinyl and removing grease from concrete without any pressure. I think the Soap Warehouse carries it.

More than one cleaner is sometimes required. I use two products on these types of grime,..I use Purple Power,..same as gutter cleaner,..and what that doesn't remove, I use Hydrochloric Acid mixed to the strength required. Purple Power works best when applied with a sprayer,...as does the acid. These jobs are also easier when it's 80-100 degrees and HUMID.

Jeff