Hi, first of all, thank you for fairly posting the values given by "Face Hard" for penetration above. It's a pleasure to discuss with a knowledgeable and polite person, even when being in disagreement.....
you wrote: "What I'm questioning is some extreme large advance of such structure over single plate."
Well, even according to "Face Hard" (and with all its limits) the advantage is quite clear giving a 16" equivalent thickness for the 13.8" combined plates of the array for "no penetration", more than justifying the complexity of the system.
So, an equivalent thickness of 406,5 mm vs 350 mm, based on the test results, that confirmed that the array plate "brilliantly resisted to the attacks" (and I suspect this estimation was cautionary).
you wrote: "Who evaluates whether the test results confirm the theory?"
I don't have any more details than the ones that are included in Bagnasco/De Toro same page that you mentioned already (I have the Italian version....). The tests were not done by Pugliese, but by another officer (Bianco di San Secondo) and final decision was taken by "Marinalles" (RM "Department for naval fittings"), according to the procedures of the RM.
you wrote: "My feelings....... is that designers expected in normal situation that some splinters, shell fragments will be thrown into the hull, so those bulkheads are placed to stop them. If splinters were not expected "
The first bulkhead (36mm) is clearly against splinters from the belt. The second (24mm) and the third one (19mm) are mainly against splinters coming from "plunging" fire hitting the outboard (weaker) part of the armor decks (or the upper belt plus the lower armor deck....). The third one is also part of the TDS. (please see scheme at pag. 12 of this thread).
The RM wanted clearly to (somehow) protect Littorio's also at very short ranges, possibly below 16 km, I would say up to 10-12 km, against guns less powerful than the Italian ones, so I would not consider "suspicious" the presence of a splinter bulkhead behind the belt, just additional protection in case of.....
If Italians really had doubts about the array functioning at that time, before starting the construction of the first two Littorio's, I think that Marinalles would have decided to build the ships with a (easier to build ) single plate of 350 mm steel, inclined 15°....... Instead, the same layout was confirmed, some time later, for the further two ships, with no change.....