The adiabatic limit is based on the assumption the heating is short-lived so essentially no significant portion heat escapes during the event (the definition of "adiabatic").
So the conductor starts at its normal temperature (which might be 20-30C for a separate CPC, or around 70C for a conductor in a set that is running at limit, etc) and during the fault the I2R term is heating the conductor for 't' seconds causing the temperature to rise until the fuse/MCB/etc disconnects. At that point the conductor is much hotter, but provided it is not so hot that the insulation is permanently damaged by such a short and occasional event the cable is OK. Depending on the type of insulation that is usually in the range of 140C to 250C.
If you know the conductor material then you can convert that change in temperature in to an I2t limit for the fault, with a bigger temperature difference allowing more heating and so a higher I2t limit.
So if you go from typical PVC upper limit of 160C (18th edition regs Table 54.2 first copper example) to bare metal with, say, 500C upper limit (Table 54.6 bare copper in "visible and restricted area" case) then your 'k' in the adiabatic equation goes from 143 to 228 and so the resulting minimum cross-sectional area goes down to 63% of the normal case (so roughly one standard cable step down, e.g. 10mm -> 6mm or 6mm -> 4mm, etc).
But that adiabatic limit is only for short lived faults like a short leading to a fuse/MCB opening. The other concern for earth conductors is the 'open PEN' fault in TN-C-S systems where you could have the local faulted segment of the network's neutral current returning via bonded service pipes, steel foundations, etc. In that case you could see tens of amps flowing for hours and the limit for conductors then is the maximum safe running temperature (basically the usual current carrying capacity).
conduit
