Grounding grid sizing: earth resistance, GPR, step and touch voltage

What grounding grid sizing is

Sizing a grounding grid is not simply burying copper conductors and driving rods: it is ensuring that, at the instant of an earth fault, no person inside or around the installation is exposed to a dangerous voltage. The design crosses three groups of data — the soil resistivity, the fault current and the grid geometry — to answer two distinct questions: what earth resistance the grid achieves, and whether the voltages that arise in the soil during the fault stay below what the human body can tolerate.

The most common conceptual mistake is to treat grounding as merely a “lower the ohms” problem. A grid can have an extremely low resistance and still be dangerous, because safety depends on the surface potential gradients, not only on the total resistance. That is why the IEEE 80 and NBR 15751 method clearly separates the resistance calculation from the safety criterion.

Geometry and the buried conductor length

It all starts with the grid geometry. The grid is a mesh of horizontal conductors of sides Lx by Ly, with spacing D between parallel cables, supplemented by vertical rods. The number of conductors in each direction is:

n_x = ⌊Lx/D⌋ + 1 ; n_y = ⌊Ly/D⌋ + 1

and the total buried length sums the mesh plus the rods:

L = (n_x·Ly + n_y·Lx) + n_rods·L_rod

This length L is decisive: the more buried conductor, the lower the resistance and the more uniform the potential. The area A = Lx·Ly defines the equivalent radius r = √(A/π), which appears in the resistance floor imposed by the soil.

Grid resistance: Sverak and Laurent

The tool computes the resistance by two methods. The Laurent-Niemann one is the simplified estimate:

R = ρ/(4·r) + ρ/L

The first term, ρ/(4r), is the resistance floor — the minimum a plate of area A would reach, regardless of how much cable is buried. The second term decreases with length. Laurent is fast and conservative, but it ignores the burial depth.

The Sverak method, adopted by IEEE 80, corrects this by capturing the depth h:

R = ρ·[ 1/L + 1/√(20·A) · (1 + 1/(1 + h·√(20/A))) ]

It is the expression recommended for design, because a grid buried deeper has lower resistance — an effect Laurent does not see. In both methods, the soil resistivity ρ is the dominant variable: doubling ρ almost doubles the resistance.

Ground potential rise (GPR)

Once the resistance is known, the GPR (Ground Potential Rise) is computed — the potential the whole grid reaches relative to remote earth during the fault:

GPR = I_G · R , with I_G = Df · Sf · I

The grid design current I_G is not necessarily the symmetrical short circuit I. The decrement factor Df (IEEE 80 §15) corrects the asymmetry in the first cycles, and the division factor Sf represents the fraction of the short circuit that actually returns through the grid (part flows via shield wires and neutrals). By default Df = Sf = 1 is adopted, throwing the whole current into the grid — the most conservative assumption.

The GPR can reach thousands of volts. It is not, by itself, the failure criterion — but it is the starting point for comparison with the safety limits.

Conductor section by the adiabatic criterion

The grid conductor must withstand the fault current thermally without melting. By the IEEE 80 adiabatic criterion (all the heat stays in the copper during the short circuit):

A_mm² = I_kA · Kf · √t · 0.5067

where Kf = 7.06 for hard-drawn copper and the factor 0.5067 converts kcmil to mm². A 50 mm² copper floor is also applied over the thermal value, required for mechanical robustness and corrosion resistance, since the conductor will stay buried for 30 to 40 years. The adopted section is the larger of the two.

The safety criterion: step and touch voltages

Here lies the heart of the design. IEEE 80 defines the maximum tolerable voltages of the human body as a function of the exposure time:

E_touch = (1000 + 1.5·Cs·ρs) · k/√t

E_step = (1000 + 6·Cs·ρs) · k/√t

The touch voltage (between the hand on a grounded structure and the feet) is the most critical limit, almost always lower than the step voltage. The coefficient k is 0.116 for a 50 kg body and 0.157 for 70 kg, and t is the fault clearing time — the longer it is, the lower the tolerable voltage.

The factor Cs represents the effect of the surface gravel layer:

Cs = 1 − 0.09·(1 − ρ/ρs)/(2·hs + 0.09)

With no gravel, Cs = 1. With a high-resistivity layer (ρs ≈ 2,000–5,000 Ω·m), Cs drops below 1, which raises the tolerable voltages — often exactly what makes a grid pass the safety criterion.

How to interpret the result

The calculation ends with a screening: it compares the GPR with the tolerable touch voltage. If GPR ≤ E_touch, the grid is classified as ok. If GPR > E_touch, the result is analyse mesh — a sign that, despite the low resistance, the potentials may be dangerous and the design needs refinement. The typical fixes are:

• Add or thicken the gravel layer (raises Cs and the tolerable voltages);
• Densify the grid (a smaller spacing D reduces the local mesh voltage);
• Increase the area or the conductor length (lowers the resistance and the GPR);
• Reduce the fault clearing time with faster protection.

Practical design considerations

• Measure the resistivity in the field (Wenner method, IEEE 81) rather than adopting a table value; the soil is stratified and ρ varies with the season.
• Do not rely on the ohms alone: the final approval is the voltage criterion, not the resistance in isolation.
• Consider the gravel layer from the start: it is usually the cheapest way to pass the touch and step voltages.
• Align standard and method: IEEE 80 and NBR 15751 govern the resistance calculation (Sverak), the GPR, the step and touch voltages and the conductor adiabatic criterion; IEEE 81 guides the resistivity measurement.

Following this chain — geometry, conductor length, Sverak resistance, GPR, adiabatic section and verification of the step and touch voltages — yields a grounding grid that protects people and agrees with the worked examples of IEEE 80.