Keep in mind the current needed to make the round trip. So .0125 ohms (sounds about right) for one way, then ??? on the return trip, as the neutral may be smaller and the ground is definitely smaller.
Then on top of that you have the hot wire going to the subpanel where the short happened, and the round-trip back on a fourth wire presumably neutral.
Oh, and then you need to account for the service drop from the utility, it will have its own wire size and length, and you'll need to calculate its resistance as well, coming and going, that is 5 and 6.
Also, at the poletop it joins a distribution wire from the transformer that has some length, so that will be resistances 7 and 8. And then we have the transformer's own effective resistance, that'll be resistance 9.
You'll need to sum all those resistances plus any resistance in the connections... before you plug the cumulative resistance into Ohm's Law.
You could test these cumulative resistances by attaching a known load to the panel where the fault occurred and measuring the resultant voltage sag. E.G. if a 36A/120V load (3 space heaters) sags voltage from 122V to 121.4V, then voltage drop is 0.6V, and plug into Ohm's Law V=IR..... 0.6=36*R solve for R.
Breaker trip curves generally call for instant trip at 600-1050% of rating (manufacturing tolerance), so we're talking 2400-4200 amps here. You could get below that pretty easily, which would lock out instant-trip and be down to thermal/inverse-time trip. That could be a second or two or longer. You can google "breaker trip curve" for examples.
Should that current not be enough to trip the breaker?
One would certainly hope so, yes... but given your long distances it may not be a fast trip.
Remember the purpose of the breaker is to trip before wires burn (i.e. get hot enough to become degraded and unfit for service going forward). So it is a race condition between the breaker's inverse-time thermal trip device and the ability of the wire to absorb heat.
Heat is stored in atoms not mass (i.e. 1 copper atom stores the same heat as 1 aluminum atom) and aluminum wire of a given ampacity has more atoms. So it can absorb more thermal energy for the same temperature rise.
Is it because the short circuit current is much lower than the interrupt rating?
No, that has nothing to do with it. This solves a different problem and a lot of engineering goes into that.
The "interrupt rating" (10kA, 22kA, 65kA, those are kiloamps so 10,000, 22,000 etc) means the limit beyond which the breaker cannot interrupt, and sits there arcing. If you used a 10kA interrupt rating, and the power company had low resistance wires that could actually deliver 18,000 amps to your meter, and you had a dead short right there, **the disconnect would see 18k amps. And the 10,000A breaker would throw up its hand and say "I can't interrupt this, best get yourself some marshmallows and graham crackers". Whereas a 22kA breaker would work.
This is decided by the service drop and distribution and transformer (resistances 5-9 above), and is the subject of a pair of rules. In residential connections, the power company must use thin enough enough wires that even a dead short at the meter cannot exceed 10kA (inclusive of transformer impedance). The other rule requires the consumer to use a 10KA rated disconnect for most residential services. (so 240 = 10000 * R, solve for R=.024 ohms, so service wiring must be at least 0.024 ohms on their side). If you ever see an installation where you look at the service wires and go "hey wait! I had to use 4/0 wire, how did they get away with #1 on the service drop?" They're not getting away with it, it's mandatory to guarantee <10kA!
However on a large 400A service, guaranteeing <10kA may not be achievable, so the power company would guarantee a higher interrupt rating such as 22kA (again 22,000 amps), and in turn you'd be required to use a 22kA rated breaker.
Or your breaker could have a 65kA rating simply because of market conditions. 400A residential services are almost always done a different way (involving dual 200A breakers), so there isn't enough demand for residential 400A breaker for economies of scale to kick in. As such, the extant 400A breakers are all industrial gear and sized for industrial applications. That's why it was so darned expensive.
Does a short circuit trip a breaker immediately or does it take time to trip it?
Like I say about trip curves... yes.
Did it not trip because the problem already existed upon connecting the power?
No, they're not that smart.
