Page 381 - Handbook of Electrical Engineering

EARTHING AND SCREENING 369

Annex A of BS7430 gives formulae for various shapes of buried conductors. See also Appendix
H of Reference 1. Reference 2 shows the mathematical derivations of some basic cases. Reference 3
provides much useful information regarding buried materials. If the rod or pipe is surrounded by a
casing or backfill of more conductive material such as Bentonite, then a lower resistance is obtained
for the same depth, the formula is:-

1 8L
R e = (ρ − ρ c ) log e − 1
2πL d

8L
+ ρ c log − 1 ohms (13.5)
e
d
Where ρ c is the back fill resistivity in ohm-metres
d is the diameter of the back fill or casing in metres.

This equation can also applied to reinforced concrete in which a steel rod is encased. A single
rectangular strip of width (ω) buried horizontally has a resistance to earth of:-

ρ 2L 2
R e = log e − 1 ohms (13.6)
2πL ωh

Where L is the horizontal length of the strip in metres
h is the depth of burial in metres.

One difficulty with a small site such as a ring main station with an overhead line pole,
a transformer and a switchgear unit is the spacing between the vertical rods tends to be small
compared with their buried length. This reduces the effectiveness of each rod due to its proximity
to the adjacent rods, see sub-section 10.2 of BS7430. The best results are obtained when the rod
spacing is approximately equal to the depth of the rod.
An arrangement of conductors for a difficult site would generally consist of a grid of horizontal
strips with vertical rods connected at the corners and sides of the grid. Hence the overall resistance
will then be a function of equations (13.4) and (13.6) (or (13.5) if necessary).
Malhothra in Reference 3, sub-section 6.12, comments that in a system comprising rods and
a horizontal grid, the rods can in some situations be deleted because they have little effect compared
with the grid acting on its own.
The current that passes into the earth causes a voltage difference across the resistance. Since
a point or region a long way from the connection to the conductor is at zero reference potential,
the connection must be at an elevated potential. This potential is called the ‘ground potential rise
or GPR’. At distances close to the point of connection the potential will be high, but further away
it will be much lower. When the earthing conductor includes a horizontal grid buried near to the
surface, the surface voltage decays in a more complicated manner. Within the grid itself are squares
or rectangles of conductors. Consequently the potential at the centre of a square or rectangle is less
than at their metallic sides. Outside the frame of the grid the decay is greater, and this creates a
region if high risk of shock. It is therefore necessary to calculate the potential at the corner of the
frame as a percentage of the full potential due to the total resistance. Two potentials are needed, the
‘corner mesh voltage or E m ’ and the ‘corner step voltage E s ’. E m and E s are obtained by calculating