Underground Duct-Bank Ampacity Derate

A duct bank is a mutual-heating problem: every loaded duct warms every other one, the heat has to reach the surface through concrete and soil, and the duct in the middle of the bank sees the worst of it. On a 3 by 3 bank fully loaded, a cable rated 285 A in the table can come back near 177 A -- roughly two conductor sizes, and a design that used the table value would run its center ducts over temperature for the life of the installation. THE DERATE FACTOR IS ENTERED, and that is deliberate: it comes from the Neher-McGrath calculation or from the NEC's Annex B tables and figures for the specific arrangement, and it depends on the cable's own thermal resistances as well as the geometry, so no geometric shortcut reproduces it and a calculator that appeared to derive one from spacing and depth alone would be inventing a number the standard owns. What IS derived here is the part geometry decides: WHICH duct governs. The image-method mutual-heating sum identifies the hottest position and reports how much worse it is than the coolest duct in the same bank -- on that 3 by 3 bank the center duct carries 24% more mutual heating than a corner -- which answers where to put the biggest circuit and explains why a bank sized on an average position fails in the middle. Soil thermal resistivity is the input the answer is most sensitive to and the one most often assumed rather than measured: a bank designed at 90 degC-cm/W and installed in 120 loses roughly another tenth of its ampacity, and a native-soil backfill is not a thermal backfill. Load factor matters for the same reason, since a bank at 100% load factor never gets the overnight cooling a 75% one does. A spare duct is only a spare until a circuit is pulled into it, so derating on today's loading is how a bank becomes overloaded without anyone changing a conductor. This does not perform the Neher-McGrath calculation, size conductors, or address short-circuit withstand, shielding and grounding, the encasement design, or separation requirements. The NEC as adopted (Article 310 and Annex B with their conditions of use), IEEE 835, the utility's standards, and the engineer of record govern.

derated ampacity = the base table ampacity times a derate factor ENTERED from the Neher-McGrath calculation or the NEC Annex B tables for the arrangement, and the table ampacity a target load requires is that relation inverted. The governing duct position is derived from the standard image-method mutual-heating sum, ln(distance to a neighbour's mirror image above grade / distance to the neighbour) summed over the other ducts.

The derate factor is ENTERED because it depends on the cable's own thermal resistances as well as the bank geometry, so no geometric shortcut reproduces it. It does not perform the Neher-McGrath calculation, size conductors, or address short-circuit withstand, conductor shielding and grounding, the concrete encasement's design, or duct bank separation requirements.

One multiplication and a published geometric sum; no NEC table or Annex B figure is reproduced.

Estimate. AHJ and licensed professional govern.

Field names used by the API: ducts_across, ducts_down, loaded_ducts, spacing_in, depth_to_top_in, base_table_ampacity_a, derate_factor, alt_derate_factor, target_load_a, derated_ampacity_a, alt_derated_ampacity_a, required_table_ampacity_a, governing_mutual_heat

• The derate factor is entered it belongs to Neher-McGrath or NEC Annex B, not to this arithmeticthe NEC as adopted and IEEE 835
• Geometry gives only the governing position the mutual-heating sum ranks ducts; it is not the deratethe engineer of record
• Soil resistivity is assumed unless measured 90 vs 120 degC-cm/W is roughly another tenth of ampacitya thermal resistivity survey