Underground Cable Ampacity: Duct Banks & Burial (Neher–McGrath)

This is the continuous, 100% load-factor form of Neher–McGrath (1957), using SI units. The thermal network follows the original paper’s equations 2, 6 and 9; earth superposition follows equations 43, 44A and 46, with the equivalent-envelope radius from Appendix II. It implements this stated model, rather than reproducing an ampacity table.

For each position, sum the self term and the image-source contribution from every other cable:

The last term is used only with an envelope; otherwise $\rho_m=\rho_e$. Real cable centres are below the isothermal ground surface and image centres are reflected above it. For envelope sides $x\le y$, let $f=(x/y)(4/\pi-x/y)$ and $r_b=(x/2)[1+(y/x)^2]^{f/2}$.

With $T_o=T_j+T_{duct}+T_e$, solve

The common ampacity is the smallest $I_p$. Sheath losses begin outside the main insulation; dielectric losses contribute half the main-insulation resistance and all outer resistances. The position table recomputes temperatures at that single common current.

Maplesoft’s open worksheet, pp. 2–5, provides a direct-burial thermal-network reference case. Its supplied resistance is used as an input; this calculator does not adopt or verify its separate skin-effect calculation. The original 1957 paper’s Appendix IV supplies a separate six-duct earth-resistance comparison.

For the reported rise from neighbouring cables, the envelope correction must also be allocated to heat sources. Equal heat per cable means the limiting cable contributes $1/N$ of the common correction and the other cables contribute $(N-1)/N$. Thus $\Delta T_{neighbours}=W_{total}[T_{mutual,p}+(N-1)T_{correction}/N]$. This attribution changes the displayed breakdown, not the common ampacity.

Identical round single-core cables, equal continuous current and uniform loss parameters at every grid position. One cable per nonmetallic duct. AC resistance, sheath-loss ratio and all internal/duct thermal resistances are supplied at the design operating conditions and remain fixed. Cable/duct lengths are effectively infinite, with two-dimensional transverse heat conduction.

The ground surface is isothermal. Soil and envelope properties are constant, with no moisture migration or drying. The envelope is centred around the grid, contains every outer cable/duct circle, and has thermal resistivity no higher than the native soil. The concrete/backfill perimeter is approximated by an equivalent isothermal cylinder. Default geometry and cable properties are illustrative design inputs, not catalogue data.

Use separated cables/ducts with centre spacing at least 1.25 outer diameters and top-row depth at least five outer diameters. This keeps the line-source/self-logarithm approximation away from touching or very shallow arrangements. For an envelope, the aspect ratio is limited to 1/3–3 and centre depth to at least twice the equivalent radius. Even within these bounds, the envelope correction is approximate; de León and Anders (2008) compare it with FEM and show geometry-dependent discrepancies.

No cyclic-load credit, transients, soil drying, layering, external heat sources, crossings, touching trefoil, magnetic ducts, armour loss, multiple cables per duct or unequal circuit loading. Frequency and bonding are represented only through the supplied AC resistance and sheath-loss ratio. A fixed resistance evaluated at the limiting temperature is used for all cable temperatures, including cooler positions. Larger sheath losses at other bonding/temperature conditions require revised input data.

Thermal ampacity does not establish an installation’s code rating or check terminations, protection, voltage drop or fault duty. Check against the standard in force. A zero portion of the sensitivity curve means dielectric losses alone exhaust the available temperature rise.