There are several recent studies that have attempted to quantify the costs. I don't have the time to locate and paste them here, but the TL;DR is that 1) yes, common law countries have much higher litigation costs; 2) the U.S. is the highest of all; but 3) while significant the differences are nowhere near enough to explain the enormous differences in infrastructure costs.
As for direct liability costs, I can't remember if I've read any recent studies of those. But I went to law school (I'm not an attorney, though) and several of my family members are tort lawyers, and I can tell you from everything I know and have learned that liability costs are overblown. The fact of the matter is that every society will force negligent businesses to internalize the costs of their negligence. Some countries (esp. common law countries) emphasize the ability of individuals to seek compensation for actual damages. Other countries emphasize prevention and enforce a much stricter regulatory regime. Either way the costs can be considerable, but in any event the U.S. doesn't stand out among developed countries AFAIK.
I just watched the Wizard of Oz this past weekend and in one of the opening scenes Miss Gulch, who was bitten by Toto, threatens to sue Dorothy's Aunt & Uncle for everything they have, taking away their farm. Point being, Americans have always had a somewhat irrational fear of litigation. It's a cultural thing. That same fear existed back in a time when building big infrastructure projects was cheap.
