Step and touch potential in mat design

Step potential is the voltage between a person's two feet, 1 m apart, when standing on the ground during an earth fault. Touch potential is the voltage between the hand touching an earthed metal structure and the feet standing on the ground. Both arise because fault current flowing into the soil makes the ground surface potential uneven.

   Earthed structure
        |  hand
        |---o   <- touch voltage = V(structure) - V(feet)
        |  /|\
  ======|==/=\==============  ground surface
        |  feet 1 m apart <- step voltage = V1 - V2
   ---- grid conductors (mat) buried ~0.5 m ----

How they are used in grid (mat) design (IEEE Std 80)

1. Tolerable limits are found first from the body current that the heart can withstand (Dalziel): $I_B = k/\sqrt{t_s}$, with $k = 0.116$ for a 50 kg person. With body resistance 1000 Ω:

$$\begin{aligned} E_{step,50} &= (1000 + 6C_s\rho_s)\,\frac{0.116}{\sqrt{t_s}} \\ E_{touch,50} &= (1000 + 1.5C_s\rho_s)\,\frac{0.116}{\sqrt{t_s}} \end{aligned}$$

where $\rho_s$ is the surface-layer resistivity, $C_s$ the surface layer derating factor and $t_s$ the fault clearing time.

2. Grid potential rise $GPR = I_G R_g$ is calculated. If GPR is below the tolerable touch voltage, the design is safe.
3. Otherwise the actual mesh voltage $E_m$ (worst touch voltage in a mesh corner) and actual step voltage $E_s$ are calculated from the grid geometry (spacing, conductor length, depth, soil resistivity).
4. The design is accepted only if $E_m < E_{touch}$ and $E_s < E_{step}$. If not, the grid is changed and the check repeated.

Why they are set this way

• Ensures that the current through a human body during the worst fault stays below the ventricular fibrillation threshold within the fault clearing time.
• Touch voltage is usually the critical one, because hand-to-feet current passes near the heart and the feet act in parallel, giving less resistance.

How they are kept within limits

• Close grid spacing and more conductors; extra rods at the perimeter.
• Surface layer of crushed rock/gravel (high $\rho_s$, about 3000 Ω·m), which raises the tolerable limits.
• Faster fault clearing (smaller $t_s$).
• Bonding all metal structures and fences to the grid; grading rings around equipment and at gates.
• Lowering grid resistance with deeper rods or treated soil.