The Contractor has failed to notify adverse weather under 60.1 (13) within 8 weeks of becoming aware. Could the PM still make an assessment but take the late notification into account or is it mandatory to obey the time bar rule? Could clause 12.3 be used to alter the contract by agreement?
Anything is possible by agreement, but they are under NO obligation to do so. I doubt you will get them to change the contract, but if you both agree nothing to stop them doing it on a case by case basis. I have seen a Z clause occasionally where the clause is amended to say at the PM’s discretion they MAY consider the effects if it is notified after the 8 weeks.
Obviously the Contractor is only time-barred on the ones THEY are obliged to notify, but unfortunately weather (along with ground conditions, lack of access etc) is one of those that is.
Cross your fingers, smile and be nice to them (although not sure any of those will help!)