Cable ampacity in a real trench: why the table does not apply

Ampacity tables are the most-used and most-misused data in cable engineering. They are exact — for the installation they describe. The moment your trench holds two rows of circuits, a thermal backfill envelope and a control cable in the corner, the table stops describing your installation, and no correction factor in the appendix puts it back. This guide shows what calculator #004 does instead, on a trench that a table genuinely cannot rate.

What the tool computes

Two things, and they answer different questions:

• The single-cable rating — Iz for one cable in its declared installation condition, per the IEC 60287 series: skin and proximity effect on Rac, dielectric losses, sheath and armour loss factors λ₁/λ₂, thermal resistances T₁…T₄, then the conductor-temperature back-calculation at your actual load and the thermal short-circuit withstand per IEC 60949.
• The trench — a cross-section you draw: soil layers with their own thermal resistivity and temperature, cables placed where they will actually lie, and a solution that accounts for every cable heating every other cable. The output is a rating per cable, its conductor temperature, and a temperature field across the whole trench.

The first is what a table gives you. The second is what a real trench needs.

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Why tables break in a multi-row trench

A published rating — IEC 60502-2 Annex B, or a manufacturer table — is one number computed for one geometry: a stated depth of laying, a stated soil thermal resistivity, a stated formation (trefoil touching, flat touching, flat spaced), and, above all, one circuit alone in undisturbed soil. Every figure in the table carries those conditions in its column heading.

Grouping factors exist, and the calculator has them: the IEC 60502-2 Annex B table B.19 set — ×0.80 for two circuits, ×0.70 for three, ×0.64 for four, ×0.60 for five, ×0.56 for six. But read what they are: a single multiplier for N circuits laid side by side, in one plane, at a stated spacing, at the table's depth, in the table's soil. They are a lookup for a standard picture. Your trench is not that picture the moment any of the following is true:

• cables sit in more than one horizontal row — the lower row is heated from above and radiates into soil that the upper row has already warmed;
• the trench has a thermal backfill envelope with a resistivity different from the native soil, so heat leaves the group through two media in series;
• spacings are unequal — a cable pushed against the trench wall behaves differently from one in the middle;
• the group is mixed — different sizes, different loads, or a control cable riding along in the same envelope;
• the burial depth differs from the table's depth, which changes T₄ for the whole group, not by a fixed ratio.

Applying a table factor anyway fails in both directions, and that is the part engineers underestimate. It can be unsafe — the hottest cable in the middle of a two-row bundle can run above the group factor's assumption, and its insulation ages accordingly. It can also be wasteful — a well-spaced two-row layout in good backfill often carries considerably more than the ×0.56 factor for six circuits suggests, and sizing to that factor buys copper nobody needed.

The honest statement of the rule: a rating table applies to the arrangement printed above it. For any other arrangement you either find a table published for that arrangement, or you compute the mutual heating. There is no third option, and interpolating between table columns is not one.

What the calculator does is the second path: T₄ for the group from the two-zone backfill model of IEC 60287-2-1, with the mutual heating of neighbours by the image method, solved per cable.

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Worked example: two rows of 240 mm² in one trench

A 1.2 m wide trench, 1.6 m deep. Native soil ρ = 1.2 K·m/W at 25 °C. A thermal backfill envelope of ρ = 0.7 K·m/W from 0.7 m to 1.1 m. Six single-core 240 mm² Cu XLPE cables, 12/20 kV, screens bonded both ends, in two rows — three at 0.8 m depth, three at 1.0 m. Conductor limit 90 °C.

Laying it out

The layout is drawn, not described: place each cable, drag it where it belongs, add soil layers with their own resistivity. Here the middle cable of the lower row is moved across the trench, and the whole layout re-renders as it goes:

The result

Press Calculate and every cable gets its own rating, its own conductor temperature, and the trench gets a temperature field:

The temperature field runs from 25.0 °C in the undisturbed soil to 66.6 °C inside the group.

What these numbers tell you

The table value is 469 A, and not one cable achieves it. That is the whole point of the exercise. The reference for 240 mm² in trefoil at the table's conditions is printed in the panel — 469 A — and the six cables in this trench rate 443 to 460 A.

The spread across nominally identical cables is 17 A. Same size, same cable, same trench — 443 A for R1-B against 460 A for R1-A. The difference is position: R1-B sits between two neighbours and receives heat from both, R1-A has open soil on one side. A single group factor cannot express this, because it returns one number for the whole group. Design to the worst cable, not to the average.

The cable that was moved got cooler. R2-B ended at x = 676 mm, away from R2-C, and rates 456 A at 75.1 °C — better than R2-C at 446 A and 77.3 °C, which stayed put next to a neighbour. This is the loop the trench editor is for: move a cable, re-solve, see whether the layout buys you capacity before the trench is dug.

Compare the two wrong answers. Take the table at face value and you get 469 A — above every actual rating, so the design is under-sized and the middle cables age faster than the specification assumes. Now apply the six-circuit group factor from table B.19 instead: 469 × 0.56 = 263 A, roughly 40 % below what this layout actually carries. Both are wrong; the second is merely wrong in the safe direction, at the cost of a cable size or two.

Derating factors of 0.59–0.62 are what the solver reports for this geometry. Notice they are not the table's 0.56 for six circuits, nor anything you could have interpolated — they come out of the geometry, the two resistivities and the depths.

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The single-cable side of the tool

The free tier is the classic IEC 60287 calculation for one cable, and it is worth knowing what it does before you trust the trench:

• Rac from R at 20 °C corrected to θmax, plus skin (ys) and proximity (yp) effects;
• Wd dielectric loss, which matters at 12/20 kV and above and is often dropped from hand calculations;
• λ₁, λ₂ sheath and armour loss factors, which depend on bonding — screens bonded both ends carry circulating current, single-point bonding does not, and the rating differs;
• T₁…T₄ thermal resistances in closed form, with the burial-depth and resistivity terms explicit;
• conductor temperature at your load, back-calculated — the answer to "the cable is rated 460 A, I am running 400 A, how hot is it";
• thermal short-circuit withstand per IEC 60949, so the same page tells you whether the conductor survives the fault it will see.

Every intermediate value is on screen, not just Iz. That is deliberate: a rating you cannot decompose is a rating you cannot defend in a design review.

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Hand check: the same cable, on paper, against a published table

A trench solution is only worth as much as the single-cable engine underneath it. So here is the check you can repeat with a pencil: take a case for which IEC publishes the answer, run it through the calculator, and do the same arithmetic by hand.

The conditions printed under IEC 60502-2:2014, Table B.2 are: maximum conductor temperature 90 °C, ground temperature 20 °C, depth of laying 0,8 m, soil thermal resistivity 1,5 K·m/W, screens bonded at both ends, ratings calculated for 6/10 kV cables. For a 240 mm² copper, XLPE, single-core cable buried direct in trefoil, that table gives 469 A.

The same case in the calculator

The same case by hand

Every step below is an equation from the IEC 60287 series, with the calculator's own geometry substituted: conductor diameter d_c = 18,5 mm, insulation thickness t1 = 3,4 mm, diameter over insulation 27,3 mm, 16 mm² copper wire screen, external diameter D_e = 32,281 mm.

1 — DC resistance at the operating temperature (IEC 60287-1-1, 2.1.1), with R20 taken from IEC 60228:

R = R20 [1 + a20 (th - 20)] = 7,54e-5 x [1 + 0,00393 x (90 - 20)] = 9,614e-5 ohm/m

2 — Skin effect (2.1.2), ks = 1 for a round stranded conductor:

xs^2 = 8 pi f 1e-7 / R = 8 pi x 50 x 1e-7 / 9,614e-5 = 1,3071
ys   = xs^4 / (192 + 0,8 xs^4) = 1,7085 / (192 + 1,3668) = 0,00884

3 — Proximity effect for three single-core cables (2.1.4.1); in touching trefoil the axial spacing is s = D_e = 32,281 mm, so d_c/s = 0,5731:

yp   = F (dc/s)^2 [0,312 (dc/s)^2 + 1,18/(F + 0,27)]
     = 0,00884 x 0,3284 x [0,1025 + 1,18/0,2788] = 0,01258
Rac  = R (1 + ys + yp) = 9,614e-5 x 1,02141 = 9,820e-5 ohm/m

4 — Dielectric loss (2.2), with e = 2,5 and tan d = 0,004 for XLPE:

C   = 2 pi e0 e / ln(Di/dc) = 2 pi x 8,854e-12 x 2,5 / ln(27,3/18,5) = 3,573e-10 F/m
Wd  = w C U0^2 tan d = 2 pi x 50 x 3,573e-10 x 6000^2 x 0,004 = 0,0161 W/m

5 — Thermal resistance of the insulation (IEC 60287-2-1, 4.1.2.1), including the ×1,07 that 4.2.4.3.3 attaches to wire-screened cables in trefoil up to 35 kV:

T1 = rho_T/(2 pi) x ln(1 + 2 t1/dc) x 1,07 = 3,5/(2 pi) x ln(1 + 6,8/18,5) x 1,07 = 0,1866 K.m/W

6 — Thermal resistance of the jacket (4.1.3), including the ×1,6 required by 4.2.4.3.3 for trefoil:

T3 = 5,0/(2 pi) x ln(1 + 2 x 1,99/28,3) x 1,6 = 0,1676 K.m/W

7 — Screen loss factor, screens bonded at both ends, trefoil (IEC 60287-1-1, 2.3.1). Screen resistance is taken at the screen temperature th_sh = 20 + 0,7 × 70 = 69 °C, mean screen diameter d = 27,8 mm:

Rs   = 1,7241e-8 / 16e-6 x [1 + 0,00393 x 49] = 1,285e-3 ohm/m
X    = 2 w 1e-7 ln(2s/d) = 2 x 314,16 x 1e-7 x ln(64,56/27,8) = 5,295e-5 ohm/m
lam1 = (Rs/Rac) / [1 + (Rs/X)^2] = 13,086 / (1 + 24,27^2) = 0,0222

8 — External thermal resistance, three single-core cables in touching trefoil with wire screens (IEC 60287-2-1, 4.2.4.3.3), u = 2L/D_e = 2 × 800/32,281 = 49,57:

T4 = 1,5 rho_T / pi x [ln(2u) - 0,630] = 1,5 x 1,5 / pi x [ln 99,13 - 0,630] = 2,841 K.m/W

9 — The rating (IEC 60287-1-1, 1.4.1.1), with n = 1, T2 = 0 and lam2 = 0 (no armour):

dth_d = Wd [0,5 T1 + (1 + lam1)(T3 + T4)]
      = 0,0161 x [0,0933 + 1,0222 x 3,0083] = 0,051 K

Iz = sqrt( (dth - dth_d) / ( Rac [T1 + (1 + lam1)(T3 + T4)] ) )
   = sqrt( (70 - 0,051) / (9,820e-5 x 3,2616) )
   = sqrt( 69,949 / 3,2029e-4 ) = 467,3 A

The three answers side by side

The hand calculation and the calculator agree digit for digit — they are the same equation chain — and both land 0,4 % under the value IEC publishes for that cable. That residual is construction data, not method: the table's cable and the calculator's generic construction differ slightly in insulation and jacket thickness, and those move T1, T3 and D_e.

The check across the whole table

One row proves little, so the same sweep was run over every size in Table B.2, in both buried formations the table publishes:

Mean deviation is 0,0 % in trefoil and +0,3 % in flat spaced. The largest single miss is 400 mm² in flat formation, where sheath circulating losses dominate the result and the table's cable almost certainly carries a larger screen than the 16 mm² assumed here.

Why this check matters more than it looks

• The formation is not cosmetic. In trefoil, the two other phases of the same circuit lie against the cable and are part of its thermal problem; the standard gives T4 = 1,5 ρ/π · [ln 2u − 0,630] for exactly that case, not the isolated-cable expression. Rate a trefoil circuit as though each cable stood alone in the soil and you land near 670 A instead of 469 A — about 40 % optimistic, and the error is invisible, because the number still looks plausible.
• λ1 depends on the formation as well. Flat formation without transposition is covered by 2.3.3, where the outer cable carrying the lagging phase has the greatest circulating-current loss. Use the trefoil expression for a flat circuit and you understate that loss and overstate the rating, with the discrepancy growing with conductor size — which is why 400 mm² flat is the worst row in the sweep.
• A table check is the cheapest audit you will ever run. Whatever software you use, take one published row, reproduce its stated conditions exactly, and compare. Land within a couple of percent and the engine implements the standard; miss by tens of percent and no amount of interface polish makes the number safe to build on.

The trench solver is this same chain with T4 replaced by superposition over the actual cable positions (IEC 60287-2-1, 4.2.3.3). That is why the worked example above can be trusted: the foundation it stands on reproduces published data.

Practical sequence

1. Compute the single-cable rating for the candidate size, so you know the ceiling.
2. Draw the trench as it will actually be built — real depths, real spacings, the backfill envelope you specified, and the cables that share it.
3. Solve, and read the worst cable, not the average.
4. If the worst cable is short, try geometry before copper: spread the rows, widen the spacing, extend the backfill envelope. Re-solve after each change.
5. Check the conductor temperature at the real load, not only at the rating — that number governs ageing.
6. Take the fault withstand from the same page, against the fault level from #002 Short-Circuit, and the voltage drop from #001 at the size you settled on.

FREE and PRO: where the line runs

For #004 the division is between one cable and a trench full of them.

FREE — open access, no account:

• the single-cable IEC 60287 rating with every intermediate on screen: R at temperature, skin and proximity effects, dielectric loss, λ₁ and λ₂, T₁ to T₄, the formation-dependent external resistance and the rating itself;
• the conductor temperature back-calculated at your actual load;
• the IEC 60949 short-circuit withstand check;
• derating for soil resistivity, ambient temperature, burial depth, formation and the number of circuits;
• the compact .docx report.

PRO:

• the Trench CAD cross-section — draw soil layers and cable positions, solve every cable heating every other one, and get the temperature field (trench_cad);
• several cross-sections in one project (multi_scenario);
• the full .docx report with the trench layout, the distance matrix, the per-cable derivation and the IEC 60502-2 cross-validation table (full_report).

One note on the trench shown in this guide: without a licence it runs as a locked showcase — Calculate works on the shipped example and the temperature field appears, but the cables, layers and IEC presets cannot be edited, and a report downloaded from the demo carries an EXAMPLE watermark. That is deliberate: the point of the demo is that you can see the mutual-heating result before deciding whether it is worth paying for.

Where this sits next to the other tools

• #001 Voltage Drop is the other half of sizing — thermal capacity and volt-drop rarely pick the same cross-section, and the larger of the two wins.
• #002 Short-Circuit gives I″k for the withstand check on the size chosen here.
• Electrical Networks carries the same cable data across a whole schematic when you have dozens of runs rather than one trench.

Open calculator #004 →