Earth resistance factors and rod earthing diameter

Factors affecting earth resistance

1. Type of soil: clay, loam and garden soil have low resistivity; sand, gravel and rock have very high resistivity.
2. Moisture content: resistivity falls sharply as moisture rises. Dry soil has very high resistivity, so earth resistance is highest in the dry season.
3. Dissolved salts (chemical content): salts make soil water conductive. Adding salt, charcoal or bentonite lowers the resistance.
4. Temperature: resistivity rises as the soil cools, very sharply when soil water freezes.
5. Size and shape of electrode: a larger plate or longer rod has more contact with soil and lower resistance. Rod length matters much more than diameter.
6. Depth of electrode: deeper electrodes reach moist, stable soil, so resistance is lower and changes less with season.
7. Number and spacing of electrodes: electrodes in parallel lower the resistance, provided they are spaced at least about twice their length apart.
8. Contact with soil: loose, dry backfill increases resistance; compacted, treated backfill reduces it.
9. Condition of electrode and joints: corrosion and loose connections increase resistance with time.

Diameter of rod electrode

For a rod (pipe) electrode driven vertically (IS 3043, written in SI units):

R = (ρ / 2πL) × ln(4L / d)

R = earth resistance (Ω), ρ = soil resistivity (Ω-m), L = length of rod (m), d = diameter of rod (m).

Given R = 10 Ω, ρ = 65 Ω-m, L = 5 m:

ln(4L/d) = R × 2πL / ρ
         = 10 × 2π × 5 / 65
         = 4.833
4L/d     = e^4.833 = 125.61
d        = 4L / 125.61
         = 20 / 125.61
         = 0.1592 m

Check: R = (65 / (2π×5)) × ln(20/0.1592) = 2.069 × 4.833 = 10.0 Ω.

Answer: Diameter of rod ≈ 0.159 m (about 15.9 cm).

Such a thick rod is not practical. Since resistance depends only weakly (logarithmically) on diameter, in practice a standard rod (16–25 mm) is made longer, or several rods are used in parallel, or the soil is treated, to get 10 Ω.