The soviets built theirs by simply embedding the wire and aluminum in concrete. I think the aluminum would need to be continuous though mesh would offer some degree of protection. I haven't built or designed a faraday in at least 2 decades but the wire and foil do work.......does it have to be grounded ? aluminium is a great conductor- how about aliminium screen?
goes the "cage" need to be isolated from whatever it touches by a non conducting material?