Ground resistance depends indeed also upon the vertical electrodes but also on horizontal electrodes-the horizontal
cable. The fault current spread into the ground radial from the grounding vertical rod or grounding horizontal electrode.
According to "Designing for a low resistance Earth Interface" [LEC, Inc] published by EES [UK] see:
there is a critical cylinder with a radius of 1.1 height of the grounding rod .If we consider under the building
a cylinder of diameter equal to building width and the height equal to h=width/2.2 then we can calculate this
cylinder resistance as grounding resistance of a rod.
Let say, there is a total substation area [included between fences] of 100 *150 ft and a building total area of
40*50 ft and ,in a permafrost condition, earth resistivity of 10^5 ohm.m .Under the building the resistivity may be
100 ohm.m [if no permafrost will be for at least 50 ft depth].
In the substation yard are 20 grounding rod of 20 ft long and a grounding grid of 15*15 ft parallel copper cables.
The outside [in the yard] total resistance will be: 1160 ohm
Calculated as a grounding rod the "under the building grid" will be approximately 850 ohm and the total resistance
[the two resistances parallel] will be 450 ohm.
I have no experience with permafrost but, as LEC company declares, one may improve the grounding rod resistance
by replacing all or part of the soil with highly conductive backfill and it will facilitates the achievement of a low-resistance ground connection. See: