How to calculate maximum short circuit current flow per second before break down?

Here find some attached circuit of three phase cabinet which operation voltage is 400V /415V and have operated current 800A, fault current for 1 sec is 46 KA and have incoming and outgoing links with one phase Lighting and socket.

I want to know is there some method that one can calculate the short circuit current per second that the bus-bar can bear.

Moreover I also want to calculate the short circuit current for 3 second.

Is there any relation between the current and time in this case (directly, or Inversely Proportion) ?

Please provide me the formula if exist to calculate short circuit current (fault-current) in any time.

Usually short circuit currents of bus bars are limited by mechanical effects. Related to fuse characteristics, it's rather unlikely to have 46 kA flowing for 1 sec. You can expect cut-off times in a ms range.

Nevertheless can you calculate maximum ∫I²t values for bus bars or cables based on the acceptable overtemperature. According to it, the 3 s short circuit current would be reduced by a factor √3.

The 46 KA I guess is the maximum current that can flow due to the impedance of the transformer feeding it. The one second could be the fusing time of the 1200A fuse protecting the 800A circuit -as FVM says its rather long. So now you put a short on your bus bar, the current will be limited a bit more by your bus bar impedance (no 46 KA), so the 1200 A input fuse will take longer to blow. So if you know your busbar impedance, just fill in the number as per I^2 T, being the same (same 1200 A or what ever input fuse)
Frank

The limit is, for certain, less than the current needed to
raise the bus-bar to the liquidus of (copper?) from its
initial temperature. A simple calculation would be the
heat mass of the bar (mass times specific heat times
temperature rise (Tliq-Tinit), for the energy allowed,
Ibus^2*Rbus*1sec for the Joule energy imparted (do
not forget to convert the heat-mass units to Joule
basis), you can solve this mess for Ibus.

Second order effects, such as the bus-bar resistance
depending on temperature, are likely to be significant.
So too, the geometry (short bar will not be adiabatic
at 1-sec timescales, a long bar will be closer if heat
can only escape meaningfully via the end connections).

And of course failure could be before liquidus, from
some other thing like the bus-bar simply softening,
slumping and shorting to the chassis or something
like that.

Please find the another attached image file in which LCC busbar also have rating 46KA at 0.5 sec.