Methods / Ground Grid

How RokBench checks this

Ground Grid Step & Touch Voltage

The IEEE Std 80 simplified method for a uniformly spaced rectangular grid in uniform soil.

1. What this check does

Computes the tolerable touch and step voltages for the body weight and shock duration you choose, the grid resistance and ground potential rise, and the mesh (worst touch) and step voltages of a rectangular grid with equal spacing, then compares them.

2. Inputs used

Soil resistivity; optional surface layer resistivity and thickness.
Grid length and width, conductor spacing, burial depth and conductor diameter; optional ground rods (count, length, on the perimeter or not).
Symmetrical ground fault current 3I0, split factor Sf, fault and shock duration, optional X/R.
Body weight 50 or 70 kg.
Optional conductor material and ambient temperature for the conductor sizing check.

3. Formulas and assumptions

Tolerable voltages

Surface layer

C_s = 1 - \dfrac{0.09\,(1 - \rho/\rho_s)}{2h_s + 0.09}

Touch

E_{\text{touch}} = \bigl(1000 + 1.5\,C_s\rho_s\bigr)\,\dfrac{k}{\sqrt{t_s}}

k = 0.116 (50 kg) or 0.157 (70 kg).

Step

E_{\text{step}} = \bigl(1000 + 6\,C_s\rho_s\bigr)\,\dfrac{k}{\sqrt{t_s}}

Grid current and resistance

Decrement

D_f = \sqrt{1 + \dfrac{T_a}{t_f}\left(1 - e^{-2t_f/T_a}\right)}, \qquad T_a = \dfrac{X/R}{2\pi f}

Grid current

I_G = D_f\, S_f\, 3I_0

Resistance

R_g = \rho\left[\dfrac{1}{L_T} + \dfrac{1}{\sqrt{20A}}\left(1 + \dfrac{1}{1 + h\sqrt{20/A}}\right)\right]

Sverak.

GPR

\mathrm{GPR} = I_G\, R_g

Mesh and step voltage

Mesh / step

E_m = \dfrac{\rho\, K_m K_i\, I_G}{L_M} \qquad E_s = \dfrac{\rho\, K_s K_i\, I_G}{L_S}

K_m = \dfrac{1}{2\pi}\left[\ln\!\left(\dfrac{D^2}{16hd} + \dfrac{(D+2h)^2}{8Dd} - \dfrac{h}{4d}\right) + \dfrac{K_{ii}}{K_h}\ln\dfrac{8}{\pi(2n-1)}\right]

K_s = \dfrac{1}{\pi}\left[\dfrac{1}{2h} + \dfrac{1}{D+h} + \dfrac{1 - 0.5^{\,n-2}}{D}\right]

Ki, Kh

K_i = 0.644 + 0.148\,n, \qquad n = n_a n_b n_c n_d, \qquad K_h = \sqrt{1 + h/h_0},\ h_0 = 1\ \mathrm{m}

Conductor size

A_{\mathrm{mm^2}} = \dfrac{I_{kA}}{\sqrt{\dfrac{\mathrm{TCAP}\times10^{-4}}{t_c\,\alpha_r\,\rho_r}\ln\dfrac{K_0 + T_m}{K_0 + T_a}}}

IEEE 80 Eq. 37 with the Table 1 material constants; I = Df × 3I0 (the conductor carries the whole fault), tc = fault duration, Ta = 40 °C unless entered.

Effective lengths

L_M = L_C + \left[1.55 + 1.22\,\dfrac{L_r}{\sqrt{L_x^2 + L_y^2}}\right] L_R \qquad L_S = 0.75\,L_C + 0.85\,L_R

LM = LC + LR when rods are not on the perimeter.

Symbols

$\rho,\ \rho_s$	Soil resistivity; surface layer (crushed rock) resistivity	Ω·m
$h_s,\ C_s$	Surface layer thickness; surface layer derating factor	m, —
$k$	Body constant: 0.116 for 50 kg, 0.157 for 70 kg
$t_s,\ t_f$	Shock duration; fault duration	s
$X/R,\ f,\ T_a$	System X/R at the fault, frequency, DC time constant	—, Hz, s
$D_f,\ S_f$	Decrement factor; current split factor
$3I_0,\ I_G$	Symmetrical ground fault current; maximum grid current	A
$A,\ L_x,\ L_y$	Grid area and side lengths	m², m
$h,\ D,\ d$	Burial depth, conductor spacing, conductor diameter	m
$L_C,\ L_R,\ L_r,\ L_T$	Grid conductor length, total rod length, one rod, total buried length	m
$L_M,\ L_S$	Effective buried lengths for mesh and step voltage	m
$n$	Effective number of parallel conductors (rectangle corrections na·nb·nc·nd)
$K_m,\ K_s$	Spacing factors for mesh and step voltage
$K_i,\ K_{ii},\ K_h$	Irregularity factor; inner-conductor and depth corrections
$R_g,\ \mathrm{GPR}$	Grid resistance; ground potential rise	Ω, V
$E_m,\ E_s$	Mesh (worst touch) voltage; step voltage	V
$\alpha_r,\ \rho_r,\ K_0,\ T_m,\ \mathrm{TCAP}$	Conductor material constants: resistivity temperature coefficient, resistivity, 1/α0 − 20, fusing temperature, thermal capacity	1/°C, µΩ·cm, °C, °C, J/cm³·°C
$t_c,\ T_a$	Clearing time for conductor sizing; ambient temperature	s, °C

Plan view of a rectangular ground grid with length Lx, width Ly, conductor spacing D and rods at the perimeter. — **Figure 1.** Ground grid plan: dimensions, conductor spacing and perimeter rods.

Cross-section showing the ground potential rise curve above a grid; a person touching a grounded structure (touch voltage) and a person walking (step voltage). — **Figure 2.** Touch and step voltage on the ground-potential profile during a fault.

Cross-section with a surface layer of thickness hs and resistivity rho-s over native soil of resistivity rho. — **Figure 3.** Crushed-rock surface layer over native soil.

Substation one-line showing fault current dividing between the ground grid and overhead shield wires or neutrals back to the source. — **Figure 4.** Only part of the fault current flows into the grid (split factor Sf).

Uniform soil. The simplified equations apply to grids with n up to 25, depth 0.25–2.5 m, spacing above 2.5 m and conductor diameter small compared with depth; outside that range a warning asks for a computer analysis.
The split factor Sf is entered by you — it depends on overhead ground wires, cable sheaths and remote grounds.
Without X/R the decrement factor is 1.0, which understates the current for short fault durations.
Worst-case touch is taken as the mesh voltage at the center of a corner mesh.
Conductor sizing follows IEEE 80 Eq. 37 with the Table 1 material constants (copper soft- and hard-drawn, copper-clad steel 40 % and 30 %, EC aluminum, 1020 steel), for the whole fault current with the decrement factor over the fault duration, from 40 °C ambient unless entered.

4. What is NOT checked

Two-layer or multilayer soil.
Touch voltage at the fence or outside the grid, and transferred potentials.
Connection (joint) temperature limits; the sizing check uses the conductor fusing temperature. Corrosion allowance and mechanical strength.
Irregular grids and unequal spacing.

5. Reference standards

Pointers only; consult the edition adopted by your authority having jurisdiction.

IEEE Std 80 — guide for safety in AC substation grounding
IEEE Std 81 — measuring earth resistivity and ground impedance
NEC 2023 Article 250 (equipment grounding, context)

6. Validation cases

These worked examples run through the engine on every change; the expected values come from the cited source. All cases: Validation.

Square grid without ground rods, 70 × 70 m grounding/grid · Standard example

Pass

Source: IEEE Std 80-2013, Annex B, Example 1 (square grid without ground rods) — Input values only. Published tolerable voltages use Cs rounded to 0.74 and Em uses Km rounded to 0.89; RokBench carries full precision, hence the small differences. For comparison the standard quotes EPRI TR-100622 at 2.67 Ω and 984.3 V.

Quantity	Expected	RokBench	Error	Result
gridResistanceOhm	2.78	2.7757	0.155%	Pass
meshVoltageV	1002.1	1001.6	0.05%	Pass
tolerableTouchV	838.2	840.5	0.274%	Pass
tolerableStepV	2686.6	2696.1	0.354%	Pass
geometry.Km	0.89	0.8896	0.045%	Pass
geometry.Ki	2.272	2.272	0%	Pass
geometry.Ks	0.406	0.4061	0.025%	Pass

Square grid with 20 perimeter ground rods, 70 × 70 m grounding/grid · Standard example

Pass

Source: IEEE Std 80-2013, Annex B, Example 2 (square grid with ground rods) — Input values only. Published values use Km rounded to 0.77; Rg by Equation (52) (Sverak), Em with the perimeter-rod effective length (Equation (91)). For comparison the standard quotes EPRI TR-100622 at 2.52 Ω, 756.2 V and 459.1 V.

Quantity	Expected	RokBench	Error	Result
gridResistanceOhm	2.75	2.7526	0.095%	Pass
meshVoltageV	747.4	749.1	0.227%	Pass
stepVoltageV	548.9	549.1	0.036%	Pass
geometry.Km	0.77	0.7717	0.221%	Pass
geometry.Ki	2.272	2.272	0%	Pass
geometry.Ks	0.406	0.4061	0.025%	Pass

Rectangular grid with 38 ground rods, 63 × 84 m grounding/grid · Standard example

Pass

Source: IEEE Std 80-2013, Annex B, Example 3 (rectangular grid with ground rods) — Input values only. Kii = 1 (grid with ground rods). The published Em back-calculates to LM = 2292.1 m, the perimeter-rod effective length of Equation (91), so onPerimeter is set. Published Em uses Km rounded to 0.77. For comparison the standard quotes EPRI TR-100622 at 2.28 Ω, 519.4 V and 349.7 V.

Quantity	Expected	RokBench	Error	Result
gridResistanceOhm	2.62	2.6185	0.057%	Pass
meshVoltageV	595.8	593.6	0.369%	Pass
geometry.conductorLengthM	1659	1659	0%	Pass
geometry.n	11.35	11.344	0.053%	Pass
geometry.Km	0.77	0.7675	0.325%	Pass
geometry.Ki	2.324	2.3229	0.047%	Pass

7. Known issues and changes

See the Engineering Notes. Try the tool: Ground Grid Step & Touch Voltage.