Resistivity equals 2 pi times spacing times voltage divided by current

Solution

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How It Works

The Wenner four-pin method drives four equally spaced electrodes into the ground in a straight line. Current flows between the outer pair, and the voltage is measured across the inner pair. Plugging those values into R = 2πSV/I gives the apparent soil resistivity at a depth roughly equal to the electrode spacing.

Example Problem

Electrodes are spaced 3 m apart. The measured voltage is 0.5 V and the applied current is 0.2 A. What is the soil resistivity?

  1. R = 2π × 3 × 0.5 / 0.2
  2. R = 6π / 0.2 = 18.85 / 0.2 = 94.25 Ω·m

A value near 100 Ω·m is typical for moist clay or loam and is moderately corrosive to buried steel.

Frequently Asked Questions

What is the Wenner method for soil resistivity?

The Wenner method places four pins in a straight line at equal spacing S. Current is injected through the outer pins and voltage is read across the inner pins. The formula R = 2πSV/I converts those measurements to apparent soil resistivity in ohm-meters. It is the standard method per IEEE 81 and ASTM G57.

Why is soil resistivity important for grounding design?

A grounding electrode must dissipate fault current safely into the earth. Low-resistivity soil (<50 Ω·m) provides good grounding; high-resistivity soil (>1,000 Ω·m) may require deep rods, chemical treatment, or ground-enhancement materials to meet safety codes.

How does electrode spacing relate to measurement depth?

In the Wenner array, the effective measurement depth is approximately equal to the electrode spacing. Increasing the spacing from 1 m to 10 m shifts the reading from near-surface soil to deeper layers, allowing you to build a resistivity profile with depth.

What are typical soil resistivity values?

Wet clay: 5-20 Ω·m. Loam and garden soil: 10-100 Ω·m. Sand: 100-1,000 Ω·m. Gravel: 1,000-5,000 Ω·m. Solid rock: 5,000-100,000+ Ω·m. Moisture content and salinity strongly affect the reading.

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