The resistance of a single earth can be calculated if the soil resistivity is known. An earth rod driven vertically, the electrode resistance can be calculated using the following formula.

where:

R = electrode resistance, Ω

ρ = Soil resistivity, Ω-m

L = Length of electrode buried in soil, m

d = Outer diameter of earth rod, m

Note: In Australia the minimum depth of vertical type earth electrode is 1.2 m [Clause 5.3.6.3, AS/NZS 3000 - 2007]

The soil resistivity at the location of the earth rod needs to be investigated. The resistivity of soils varies with

1. the depth from the surface,
2. the type and concentration of soluble chemicals in the soil,
3. the moisture content, and
4. the soil temperature.

In other words, the soil resistivity is dependent on the electrolyte in the soil. The presence of surface water does not necessarily indicate low resistivity.

In the absence of soil investigative data, typical resistivity of various soil types is given in the following table.

Typical soil resistivity (IEEE 142)

Soil Type Average Resistivity Ω-m
Poorly graded gravel 1000 - 2500
Clayey gravel 200 - 400
Silty sand 100 - 800
Clayey sands 50 - 200
Silty or clayey sand with slight plasticity 30 - 80
Fine sandy soil 80 - 300
Gravelly clays 20 - 60
Inorganic clays of high plasticity 10 - 55

Example:

Soil resistivity = 180 Ω-m

Earth rod = ø19mm x 1.8 m

Solution:

Assuming that the earth electrode is fully driven into the ground, the resistance will be

In the event that the desired soil resistivity is not achievable using a single earth electrode, multiple electrodes could be used. The multiplying factors for multiple electrodes are given in the following table

Multiplying Factor of Multiple Electrodes(IEEE 142)

Number of electrodes Factor
2 1.16
3 1.29
4 1.36
8 1.68
12 1.80
16 1.92
20 2.00
24 2.16

References

1. IEEE 142 (Green Book) 2007IEEE Recommended Practice for Grounding of Industrial and Commercial Power Systems
2. Practical Grounding, Bonding, Shielding and Surge ProtectionG. Vijayaraghavan, Mark Brown, Malcolm BarnesNewnes 2004 - IDC Technologies
3. AS/NZS 3000 - 2007 Wiring Rules

## Author

• A Filipino Engineer, Registered Professional Engineer of Queensland (RPEQ) - Australia, and Professional Electrical Engineer (PEE 2574 - 1st Place April 1991) - Philippines with extensive experience in concept selection, front-end engineering, HV & LV detail design, construction, and commissioning of Hazardous and Non-Hazardous Area electrical installations in water and wastewater pipeline and pumping facilities, offshore platforms, hydrocarbon process plants and pipelines including related facilities. Hazardous area classification and design certification (UEENEEM015B, UEENEEM016B, UEENEEM017B).

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