Worked Example: Mining Trailing Cable — 500 m Dragline Supply at 11 kV

This example reveals the single most underestimated parameter in mining cable design: soil thermal resistivity. Standard cable sizing assumes soil thermal resistivity of 1.0 K·m/W (the IEC reference value for moderately moist clay). Mine spoil — the broken rock, overburden, and coal fines that fill active mining areas — has a thermal resistivity of 2.5 to 5.0 K·m/W when dry. This 2.5–5× difference can force a cable upsize of 2–3 cross-section steps, adding hundreds of thousands of dollars to the cable cost.

For an 11 kV three-phase supply at maximum demand:

I_FL = P / (√3 × V × PF) — (Eq. 1)

I_FL = 28,000,000 / (√3 × 11,000 × 0.85)

I_FL = 28,000,000 / 16,187

I_FL = 1,730 A

For average demand:

I_avg = 18,000,000 / (√3 × 11,000 × 0.88) — (Eq. 2)

I_avg = 18,000,000 / 16,764

I_avg = 1,074 A

The cable must be rated for the maximum demand current of 1,730 A, which occurs during the peak digging cycle (bucket loaded, hoisting at full speed, simultaneous swing).

The dragline operates in a repetitive cycle of approximately 60 seconds. The RMS current over the cycle determines the cable thermal loading:

I_RMS = √((I_peak² × t_peak + I_high² × t_high + I_med² × t_med + I_low² × t_low) / T_total) — (Eq. 3)

Using typical cycle profile:

I_RMS = √((1,730² × 10 + 1,400² × 15 + 1,100² × 20 + 600² × 15) / 60)

I_RMS = √((29,929,000 + 29,400,000 + 24,200,000 + 5,400,000) / 60)

I_RMS = √(88,929,000 / 60)

I_RMS = √(1,482,150)

I_RMS = 1,218 A

The RMS current of 1,218 A represents the sustained thermal equivalent of the cyclic loading. Some standards permit sizing the cable for the RMS current rather than the peak current when the duty cycle is well-defined.

First, size the cable assuming the IEC reference soil thermal resistivity of 1.0 K·m/W to establish a baseline.

AS/NZS 1802 Clause 5.3 specifies current ratings for mining trailing cables. Reference conditions: 40°C ambient, in air.

Ambient temperature correction (k₁):

From AS/NZS 3008 Table 22 (referenced by AS/NZS 1802), Row 45°C, Column 90°C EPR:

k₁ = 0.95

Installation correction — surface lay:

Trailing cable on ground surface, direct sun. AS/NZS 1802 Clause 5.3.2.1 specifies a solar radiation derating factor:

k_solar = 0.90

No grouping (single trailing cable): k₂ = 1.00

Combined derating (surface):

k_{total,surface} = 0.95 × 0.90 = 0.855 — (Eq. 4a)

Required ampacity for peak demand:

I_z = 1,730 / 0.855 = 2,024 A

Required ampacity for RMS (cyclic duty):

I_z,RMS = 1,218 / 0.855 = 1,424 A

From AS/NZS 1802 Table 5.1 (trailing cable, 11 kV, three-core EPR copper, in air):

For peak demand: 630 mm² (surface lay, standard soil, air ratings).

For RMS cyclic duty: 300 mm² (if cyclic rating is accepted).

IEC 60502-2, Table C.1 provides current ratings for three-core cables. Reference conditions: 30°C ambient, in air.

Ambient temperature correction:

From IEC 60364-5-52 Table B.52.14, Row 45°C, Column 90°C EPR:

C_a = 0.87

Solar radiation derating:

k_solar = 0.90 (consistent with AS/NZS)

Combined derating:

C_total = 0.87 × 0.90 = 0.783 — (Eq. 4b)

Required ampacity:

I_z = 1,730 / 0.783 = 2,210 A

From IEC 60502-2 Table C.1 (three-core, 11 kV, EPR, copper, in air at 30°C):

IEC selection: 630 mm² (same as AS/NZS for surface conditions).

For mining applications, NEC Article 590 (Temporary Installations) and MSHA 30 CFR Part 75 govern cable selection.

Temperature correction for 45°C ambient from NEC Table 310.60(C)(4):

C_a = 0.90 (40°C base, 90°C insulation)

Combined with solar correction:

C_total = 0.90 × 0.90 = 0.810 — (Eq. 4c)

I_z = 1,730 / 0.810 = 2,136 A

From NEC Table 310.60(C)(69), three-core shielded MV cable in air:

NEC selection for surface: 1000 kcmil (507 mm²).

Now recalculate for the actual burial conditions: cable partially buried in mine spoil at 1.5 m depth with soil thermal resistivity of 3.5 K·m/W (measured average) and 5.0 K·m/W (worst-case dry summer).

The burial derating fundamentally changes the cable selection. The cable’s current rating when buried is a function of the thermal circuit from conductor to ambient, and soil thermal resistivity is the dominant thermal resistance in this circuit.

The cable current rating when buried is calculated using the IEC 60287 methodology:

I = √((θ_c − θ_a) / (R_c × (T₁ + T₂ + T₃ + T₄))) — (Eq. 5)

Where:

For a 630 mm² three-core 11 kV cable: overall cable diameter d_e ≈ 125 mm, burial depth D = 1.5 m.

T₄ at different soil thermal resistivities:

T₄ = (ρ_soil / (2 × π)) × ln(2 × 1.5 / 0.125) — (Eq. 6)

T₄ = (ρ_soil / 6.283) × ln(24)

T₄ = ρ_soil × 0.506

For a cable where T₄ is approximately 50% of total thermal resistance:

k_soil = √(T_total,ref / T_total,actual) — (Eq. 7)

k_soil(3.5) = √(1.012 / 2.277) = √(0.444) = 0.667

k_soil(5.0) = √(1.012 / 3.036) = √(0.333) = 0.577

630 mm² cable ratings adjusted for mine spoil:

The 630 mm² cable that was adequate on the surface (2,180 A in air) is dramatically inadequate when buried in mine spoil. At 3.5 K·m/W, its buried rating drops to only 1,027 A — 59% of the required 1,730 A.

For peak demand (1,730 A) buried at 1.5 m in 3.5 K·m/W spoil:

I_z,required = 1,730 / k_soil(3.5) = 1,730 / 0.667 = 2,594 A (equivalent rating in reference soil)

No standard three-core 11 kV trailing cable exists at this rating. The maximum standard size is typically 630 mm² (rated approximately 1,540 A buried in reference soil).

Solution options:

1. Parallel cables: Use two parallel 500 mm² cables, each carrying 865 A. At 3.5 K·m/W, a single 500 mm² cable buried has a derated rating of approximately 890 A. Two cables in parallel: 2 × 890 = 1,780 A. PASS (barely).

2. Thermal backfill: Replace the mine spoil around the cable with controlled thermal backfill (CBS: cement-bound sand) with thermal resistivity of 0.75–1.0 K·m/W. This restores the cable rating to near-reference conditions.

3. Route on surface: Keep the cable on the surface where air cooling provides much higher ratings (2,180 A for 630 mm²). Standard practice for dragline trailing cables but not always possible in active pit areas.

4. Use RMS cyclic rating: If the mine accepts sizing for the RMS duty cycle current (1,218 A) rather than the peak demand:

I_z,RMS,buried = 1,218 / 0.667 = 1,826 A (reference soil equivalent)

A single 630 mm² cable with buried reference rating of 1,540 A still fails. But with the cyclic duty credit and partial surface routing, the solution may be feasible.

At 11 kV and 500 m, voltage drop is significant even for MV cables:

ΔV = √3 × I × L × (r × cos(φ) + x × sin(φ)) / 1000 — (Eq. 8)

630 mm², 500 m, 1,730 A, PF 0.85:

From IEC 60502-2, 630 mm², 11 kV, three-core:

r = 0.0366 mΩ/m (at 90°C), x = 0.080 mΩ/m

ΔV = 1.732 × 1,730 × 500 × (0.0366 × 0.85 + 0.080 × 0.527) / 1000

ΔV = 1,497,580 × (0.0311 + 0.0422) / 1000

ΔV = 109.8 V = 1.00% (of 11,000 V)

Within the typical mining limit of 5%. PASS.

Parallel 500 mm² cables (each carrying 865 A):

r_eff = 0.0463 / 2 = 0.0232 mΩ/m, x_eff = 0.080 / 2 = 0.040 mΩ/m

ΔV = 1.732 × 1,730 × 500 × (0.0232 × 0.85 + 0.040 × 0.527) / 1000

ΔV = 1,497,580 × 0.0408 / 1000

ΔV = 61.1 V = 0.56%

Lower voltage drop, as expected for the larger total cross-section.

The cable must withstand the prospective short-circuit current at the pit-edge switchyard for the duration of the protection clearance time.

Typical mining 11 kV fault level: 250 MVA (I_sc = 13.1 kA). Protection clearance time: 0.5 seconds.

Adiabatic equation for 630 mm² copper, EPR (k = 143):

k² × S² = I² × t — (Eq. 9)

I_max = k × S / √t = 143 × 630 / √(0.5) = 90,090 / 0.707 = 127,405 A

The cable can withstand 127.4 kA for 0.5 seconds, far exceeding the 13.1 kA fault level. PASS.

For parallel 500 mm² cables:

I_max = 143 × 500 / √(0.5) = 71,500 / 0.707 = 101,100 A

Still far exceeds 13.1 kA. PASS.

The copper wire braid screen must carry earth fault current for the protection clearance time. For a mine 11 kV system:

Earth fault current (solid): I_ef = 500 A (restricted earth fault, Petersen coil earthed system). Clearance time: 2.0 seconds.

S_screen = I_ef × √t / k = 500 × √(2.0) / 143 — (Eq. 10)

S_screen = 500 × 1.414 / 143

S_screen = 4.95 mm²

A minimum 6 mm² equivalent copper wire braid screen is required. Standard mining trailing cables typically have 16–25 mm² screen cross-section, providing ample margin. PASS.

The key finding in this example is that soil thermal resistivity at mining depth completely dominates cable selection — and most engineers use the wrong value by a factor of 2 to 5×. Standard cable rating tables assume soil thermal resistivity of 1.0 K·m/W, which represents moderately moist clay. But mine spoil is neither undisturbed, nor clay, nor moist.

Mine spoil consists of broken rock fragments, coal fines, sand, and overburden material that has been excavated, trucked, and dumped in loose fill. The void spaces between fragments are filled with air (an excellent thermal insulator), and in arid mining regions, the moisture content can drop to near zero during summer drought. Measured thermal resistivities of mine spoil range from 2.5 K·m/W (typical, slightly moist) to 5.0 K·m/W (dry summer) to as high as 7.0 K·m/W (completely desiccated coal fines).

The practical impact is devastating: a cable sized using the standard 1.0 K·m/W reference value has a buried current rating that is 45–70% too high. A 630 mm² cable that the tables say can carry 1,540 A buried can actually only carry 889–1,027 A in mine spoil. If the engineer does not perform a site-specific thermal resistivity survey (which costs approximately $5,000–10,000), the cable will overheat, the EPR insulation will degrade, and the cable will eventually fail.

AS/NZS 1802 is the only standard among the three that explicitly addresses mine spoil thermal resistivity with specific guidance (Clause 5.3.3). IEC 60502-2 provides the calculation methodology (via IEC 60287) but leaves the soil resistivity value entirely to the engineer. NEC provides correction factors in Table 310.60(C)(4) but does not address mine spoil specifically.

The cost implication is enormous: going from a single 630 mm² cable ($350,000) to parallel 500 mm² cables ($560,000) represents a 60% cost increase — approximately $210,000 in additional cable for a single dragline feed. For a mine with 10 draglines, each with 2–3 trailing cables, the total additional cable cost can exceed $4 million. Against this, the cost of a cable failure (unplanned dragline downtime at $200,000–500,000 per day, cable replacement, potential fire risk in the pit) is far greater. The $5,000–10,000 soil thermal resistivity survey is among the highest-ROI engineering investments in mining electrical design.