Duct Bank

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There is not a simple formula but a proceeding.
You have to know a few details of the cable as conductor diameter, insulation thickness, cable core assembly diameter, shield-if any-details, jacket thickness and overall diameter.
You could follow the NEC recommendations-see art.310 if the NEC meets your conditions-earth temperature, earth RHO, duct no.and position and so on. If not, you may proceed as per Neher and McGrath method "The Calculation of the Temperature Rise and Load Capability of Cable Systems".
 
Computer programs are best suited for doing the calcs. Many factors to consider, as stated.

But the information needed does not change, other than the program may have library info to help.

You must also have some inclination of soil type, depths of duct bank, finished grade surface material, and obviously the loading of the cable.
 
Take a few minutes and browse through "Informative Annex B" in the back of the code book..
For a common service entrance and somewhat conservative number, see Table B.310.15(B)(2)(7)...
Many use the RHO 90 and Load Factor 100 column, although these tables and
info are usually referred to by the engineers...
 
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