Liability can also come into play if they've had these things pull out of the road before, in which case it can be argued that they ought to continually try to clear these things up. File in small claims court (up here, they can't award "costs" in small claims). Offer to settle for the cost of the repair, or let them pay their legal team to build a case to defend themselves, and let them pay their lawyers to show up in court to defend themselves.
I work for a public agency, and when threatened with a lawsuit, every time there's a decision of whether to simply reimburse or to let it go to court. Most often, we reimburse-- but usually only when we expect the other party will take it to court.
You can be held liable for damage, even if you didn't know anything was wrong-- if I build a building, and after 15 years with no prior warning, a window on the top floor blows out in a windstorm and hits somebody below, I do have liability for the damages that person suffers, whether I'm a private individual or the government. If I was aware that something had been going wrong, and I did nothing about it, then I could face criminal charges.
That said, there is a "reasonable expectation" issue-- we don't expect roads to be completely clear. But who's really expecting big chunks of . If you're walking in a grocery store, and you slip and fall on a tomato that somebody dropped on the floor, is the grocery store at fault? Maybe, maybe not-- as long as they do periodic clean-ups, they won't be at fault, because it's a normal expectation that fruits will occasionally be dropped on the ground.
On a road, who really expects a big cast iron road marker to come out of the road and blow through the bottom of their car? File the paperwork, as Flank says, and see where it goes.