Just to throw some little needed support Al's way,
Clause 4 is there to enable the contractor to get a procedure approved by testing that is not already 'Pre-Approved' by past history. Things like processes: GTAW, GMAW-S, etc. Things like materials not listed in Table 3.1 for whatever reason. Things like material that is outside the normal scope of D1.1 as specified in Clause 1.2 and other places for tensile and/or yield strength. And other similar situations.
So you may indeed qualify your material and thus your procedure by testing per Clause 4 of D1.1:2010.
He Is In Control, Have a Great Day, Brent