Soil resistivity
Apparent soil resistivity from Wenner readings (two spacings)
- where
- apparent resistivity at each spacing (Ω·m)
- probe spacings (m)
- measured resistance V/I at each spacing (Ω)
- probe depth (m)
Explain this equation
Converts Wenner four-probe resistance readings into apparent soil resistivity at two spacings, to show whether resistivity changes with depth before choosing a soil model.
a is the equal spacing between the four probes and R the measured voltage-to-current ratio. b is the probe depth; the two square-root terms correct for probes that are deep compared with the spacing. When b is small the denominator becomes 2 and the result is the familiar 2πaR.
The geometry comes from the potential of point current sources and their images in the ground surface. A wider spacing drives current deeper, so the apparent resistivity at spacing a mostly reflects the soil down to about a.
A reading of 40 Ω at 1 m spacing is about 250 Ω·m. If the apparent resistivity at 16 m is much lower than at 2 m, the lower layer is more conductive and long rods or deep electrodes will pay off.
Watch out: apparent resistivity is not the layer resistivity. Fitting a two-layer model needs readings at many spacings and curve matching or software.
Converts Wenner four-probe resistance readings at two spacings into apparent resistivity, to show whether the soil is layered.
Enter your values to see the result.
Good to know
For probes much shallower than the spacing (b < a/10) the expression reduces to ρ = 2πaR. Apparent resistivity at spacing a reflects the soil down to roughly a depth of a. Take readings at several spacings (for example 1, 2, 4, 8, 16, 32 m) on two perpendicular traverses; a steady rise or fall indicates a two-layer soil. Example: a = 1 m, R = 40 Ω gives about 251 Ω·m.
Common mistake
Treating the apparent resistivity at one spacing as the soil resistivity. A single reading in layered soil can be badly misleading for grid design.
Limits
Gives apparent resistivity only. Fitting the upper-layer resistivity, lower-layer resistivity and layer depth needs curve matching (IEEE 81, IEEE 80 Annex E, Tagg/Sunde curves) or inversion software, which is not done here. Buried metalwork and HV interference distort readings.
Sources
- IEEE Std 81-2012 Guide for Measuring Earth Resistivity, Ground Impedance, and Earth Surface Potentials of a Grounding System
- IEEE Std 80-2013 Guide for Safety in AC Substation Grounding
- BS 7430:2011+A1:2015 Code of practice for protective earthing of electrical installations (withdrawn 2026, replaced by a revised edition)
- BS EN 50522 Earthing of power installations exceeding 1 kV a.c. (2010; superseded by EN 50522:2022)
For competent high-voltage engineers. Results are calculations from the published methods shown and depend entirely on the data you enter. They are not a substitute for a system study, manufacturer data, the applicable standards and Engineering Recommendations, or your organisation’s safety rules. Never use a result to justify working on or near live HV equipment.