Have you watched Ken Burn's Civil War series? They talk a little about the siege of St. Petersburg and I figure you must be referring to that.

The one big improvisation they talk about in that fight was the use of underground tunnels to deliver dynamite to enemy positions, and when that dynamite went off, they blew a massive hole in the Confederate lines that could have caused a bad defeat for the CSA- but the Union bungled it, as usual, by trying to use the crater as a foothold instead of going around it. So they sent hundreds of guys into a crater, with no ladders, and expected them to advance. That was a miserable turkey shoot, predictably. Other than that I don't remember any mentions of other improvisations. If they couldn't figure out how to exploit a breach in a trench I doubt they got very good at the rest of the business.

But if history is any indication, there probably wasn't any postwar attempt to design equipment specifically for trench warfare. Back then all anyone cared about was Napoleonic tactics, even after the invention of the rifle completely screwed with them. The siege was an unusual case in a war mostly defined by lines and lines of soldiers and cannon, and European observers reacted to the American Civil War not by recognizing the impact of the rifle, but instead smirking and basically saying "Aww, that's cute. The Americans don't know how to fight a war." So St. Petersburg went down as a nasty episode culminating in an attack where the Union failed to exploit a breach they made with dynamite, but I doubt anybody was really paying attention and going "Uh, will this be a trend or something that we should prepare for?" Even the Siege of Port Arthur didn't bother anyone.