🎓 Lesson 14
D5
Step & Touch Potential Calculations for High-Soil-Resistivity Sites
Step and touch potential are measures of how much electric voltage a person could feel between their feet (step) or between their hand and feet (touch) during a lightning strike or fault on grounded mine infrastructure — especially dangerous where the soil doesn’t conduct electricity well.
🎯 Learning Objectives
- ✓ Calculate step and touch potentials for a given grounding electrode system using soil resistivity and fault current data
- ✓ Design a graded-gravel surface layer and ground grid layout to reduce hazardous potentials at high-resistivity mine sites (ρ > 1000 Ω·m)
- ✓ Analyze the impact of soil layering (e.g., thin topsoil over bedrock) on potential distribution using the Schwarz equation
- ✓ Explain the role of surface layer resistivity (ρs) and thickness (hs) in mitigating touch voltage per IEEE Std 80
- ✓ Apply IEEE Std 80 safety limits to evaluate compliance for personnel working near HV substations or lightning-protected blast monitoring systems
📖 Why This Matters
In remote mining operations — especially arid, rocky, or lateritic terrains — soil resistivity often exceeds 3000 Ω·m. When lightning strikes a power pole or a grounding fault occurs in a 33-kV mine distribution network, dangerously high step and touch voltages can develop across bare ground or equipment enclosures. In 2021, a fatality occurred at a Western Australian iron ore site when a technician stepped near a grounded lightning arrestor during a thunderstorm — post-incident analysis confirmed step potential exceeded 5.5 kV due to unmitigated high-resistivity soil. Understanding and controlling these potentials isn’t theoretical: it’s a life-safety requirement mandated by MSHA, IEC, and IEEE.
📘 Core Principles
Step and touch potentials originate from the non-uniform dissipation of fault current into the earth. In uniform soil, voltage decays radially from the electrode; however, in high-resistivity settings (e.g., granite bedrock with ρ = 5000 Ω·m), current crowds near the surface, increasing gradients. The presence of a high-resistivity surface layer (e.g., crushed rock, ρs ≈ 3000 Ω·m) paradoxically *reduces* touch potential by limiting current flow through the body — but only if properly designed per IEEE Std 80’s ‘surface layer correction factor’. Soil layering, electrode geometry (counterpoise vs. driven rod), and fault duration (e.g., 0.5 s relay clearing time) all critically affect the peak potential. Real mine sites often feature complex stratification: 0.3 m of dry laterite (ρ₁ = 4000 Ω·m) over fractured basalt (ρ₂ = 800 Ω·m), requiring multi-layer modeling via the Schwarz method rather than simplified uniform-earth assumptions.
📐 Key Calculation: Touch Potential (IEEE Std 80)
The maximum allowable touch potential for a 50 kg person is calculated per IEEE Std 80–2013, incorporating surface layer derating. This formula accounts for both body resistance and the protective effect of high-resistivity gravel surfacing.
Maximum Allowable Touch Voltage (IEEE Std 80–2013)
E_touch = (ρ × Kₜ × Kₛ × I_G) / (L_T × √t_c) × CₛCalculates the maximum tolerable voltage between grounded structure and nearby earth surface for personnel safety.
Variables:
| Symbol | Name | Unit | Description |
|---|---|---|---|
| ρ | Soil resistivity | Ω·m | Average resistivity of native soil to depth of grid burial |
| Kₜ | Surface layer derating coefficient | dimensionless | Function of surface layer thickness and resistivity; typically 0.11–0.17 for hs = 0.075–0.3 m |
| Kₛ | Geometric spacing factor | dimensionless | Depends on grid conductor spacing, depth, and mesh size; ranges 0.4–0.8 for typical mine grids |
| I_G | Maximum grid fault current | A | RMS symmetrical current flowing into ground grid during worst-case fault |
| L_T | Total buried conductor length | m | Sum of all horizontal and vertical grounding conductors in the system |
| t_c | Fault clearing time | s | Time from fault inception to relay-tripped isolation |
| Cₛ | Surface layer correction factor | dimensionless | Cₛ = 1 − 0.09(1 − ρs/ρ); accounts for protective effect of high-resistivity surface layer |
Typical Ranges:
Arid granite terrain (e.g., Pilbara): 3000 – 8000 Ω·m
Crushed granite surface layer: 2500 – 5000 Ω·m
Mine substation fault duration: 0.2 – 0.5 s
💡 Worked Example
Problem: A surface-mounted lightning protection ground grid at a gold mine in Nevada experiences a 12 kA, 0.3 s symmetrical fault. Soil resistivity ρ = 4200 Ω·m. A 0.15 m thick crushed granite surface layer (ρs = 3500 Ω·m) covers the area. Calculate the maximum allowable touch voltage and compare to actual computed touch potential of 3.8 kV.
1.
Step 1: Compute surface layer derating factor Cₛ = 1 − (0.09 × (1 − ρs/ρ)) = 1 − (0.09 × (1 − 3500/4200)) = 1 − (0.09 × 0.167) = 0.985
2.
Step 2: Apply IEEE Std 80 Eq. (37): E_touch = (ρ × Kₜ × Kₛ × I_G) / (L_T × √t_c), where Kₜ = 0.157 (for 0.15 m gravel), Kₛ = 0.66 (for grid geometry), I_G = 12,000 A, L_T = 180 m (total conductor length), t_c = 0.3 s → E_touch = (4200 × 0.157 × 0.66 × 12000) / (180 × √0.3) = 3,290 V
3.
Step 3: Apply Cₛ correction: E_touch_corrected = 3290 × 0.985 = 3,241 V. Compare to actual measured value of 3,800 V → exceeds limit by 17%, requiring mitigation.
Answer:
The corrected allowable touch voltage is 3.24 kV. Since the actual potential is 3.8 kV, the design fails IEEE Std 80 compliance and requires additional ground rods or increased gravel thickness.
🏗️ Real-World Application
At the Tasiast Gold Mine (Mauritania), engineers faced persistent step potential hazards (>4.5 kV) near the 132-kV substation during seasonal thunderstorms. Site soil testing revealed ρ = 6200 Ω·m (granite) with no natural surface layer. Mitigation included: (1) installing a 0.25 m thick crushed dolerite surface layer (ρs = 4800 Ω·m), (2) extending the ground grid with 60-m counterpoise rings spaced at 3-m intervals, and (3) adding 24 vertical 3-m copper-bonded rods tied to the grid. Post-installation measurements confirmed step potential reduced from 4.7 kV to 1.1 kV — achieving <1.3 kV (IEEE 80 limit for 0.3 s fault). This solution was validated using CDEGS software and accepted by MSHA during the 2022 infrastructure audit.