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Surface layer and Cs

A surface layer is a layer of crushed rock, of high resistivity, spread over the soil of the switchyard. It adds resistance at a person's feet and so raises the tolerable touch and step voltages (IEEE Std 80-2013 §7.4).

Read first: Tolerable body current

1The layer at a person's feet

The contact resistance of one foot is $3 C_{s} ρ_{s}$ , where $ρ_{s}$ is the layer's resistivity (Tolerable body current, From current to voltage). A layer of higher resistivity than the soil raises that resistance, so the same body current needs a higher voltage. The design takes a layer of 3000 Ω·m and 0.10 m by default, set on the Site & soil page.

2The derating factor

Over a soil of lower resistivity, a layer of finite depth gives a lower resistance at the feet than a deep layer of its own resistivity. The derating factor $C_{s}$ corrects the layer's resistivity for its depth.

C_{s} = 1 - \frac{0.09 ( 1 - ρ / ρ _{s} )}{2 h _{s} + 0.09}

(1)

IEEE Std 80-2013 §7.4, Eq. 27

where
$C_{s}$	surface layer derating factor
$ρ$	resistivity of the soil below the layer	Ω·m
$ρ_{s}$	resistivity of the surface layer	Ω·m
$h_{s}$	depth of the surface layer	m

$C_{s}$ is 1 when the layer's resistivity equals the soil's, since the numerator is then zero. It rises towards 1 as the layer deepens (Figure 1). With no surface layer, a depth of 0 m, the design takes $C_{s}$ = 1. In a two-layer soil, $ρ$ is the upper layer's resistivity with the season factor (Two-layer soil, How the design uses the layers).

Layer depth0.150 m · ρs 3000 Ω·m: 0.781 · ρs 1000 Ω·m: 0.804

Figure 1.The derating factor rises with the depth of the surface layer, for layers of 1000 Ω·m and 3000 Ω·m over soil of 150 Ω·m. The design service calculated the values by Eq. (1).

Example 1The derating factor of the default 220 kV project

Given soil of 150 Ω·m below a layer of 3000 Ω·m and 0.10 m.

Derating factor by Eq. (1):

C_{s} = 1 - \frac{0.09 ( 1 - 150 / 3000 )}{2 \times 0.10 + 0.09} = 0.705

Result The layer's effective resistivity at the feet is 0.705 of its own. The tolerable touch voltage is 685 V and the tolerable step voltage 2246 V (Tolerable body current, Example 1).

Sources

[1]IEEE Std 80-2013, IEEE Guide for Safety in AC Substation Grounding. §7.4, Eq. 27.

CitationSubstationLayout Reference, Surface layer and Cs, revision 1, 8 Nov 2026, https://substation.solarlayout.app/library/reference/surface-layer

Surface layer and Cs

1The layer at a person's feetCopy link to The layer at a person's feet

2The derating factorCopy link to The derating factor

1The layer at a person's feet

2The derating factor