NEW ORLEANS — A team of plaintiffs’ attorneys has spent roughly $16 million to sue the Army Corps of Engineers over levee breaches that flooded most of New Orleans after Hurricane Katrina. Joseph Bruno, one of those lawyers, estimates that they ultimately will recoup a mere $3.5 million of their investment.

There won’t be any windfalls for their clients, either. A string of court rulings has insulated the federal government from liability for billions of dollars in flood damage that many residents and business owners have blamed on the corps’ shoddy design, construction and maintenance of the region’s system of levees and floodwalls.