Did General Zod do this?

We haven’t seen anything official in terms of what General Zod or Superman’s outfits will look in Zack Snyder’s Man of Steel, but we’ve seen plenty of on-set destruction left in their wake.

Did General Zod smash some stuff up or what?

The source seems to think this damage is from a physical fight between Zod and Superman, something they seem to think the film will have a lot of. General Zod will be played by Michael Shannon and Superman is UK unknown (well, until Immortals hits) Henry Cavill.

Source: Superman Homepage