Soil Resistivity: Schlumberger and Other Methods

Short answer. Soil resistivity is measured with four probes in a line. If they are equally spaced it is called the Wenner method; if the inner ones are closer together than the outer ones, Schlumberger-Palmer. A third option is depth variation: the resistance of a rod is measured as it is driven deeper. IEEE Std 81-2012 (clause 7) describes all three and explains how to interpret the results. This article focuses on the unequal-spacing array and on depth variation, and takes Wenner only as a point of comparison.

What apparent resistivity is

Soil is almost never uniform. It has layers with different resistivities, and these depend on soil type, temperature, moisture, mineral content and compaction. The guide cites values ranging from less than 1 Ω·m for seawater to 10⁹ Ω·m for sandstone. For that reason each measurement gives an apparent resistivity: the equivalent resistivity of a volume of soil with varying properties. The curve of apparent resistivity against spacing or depth is what reveals the structure of the soil.

Geological information and samples

Before measuring, clause 7.2.1 recommends gathering what is already known about the site. If geotechnical studies exist, it is useful to obtain the soil type of each layer, the moisture content, the pH and the depth of the water table. Measuring the resistance between opposite faces of a sample of known dimensions is not recommended: it includes unknown contact resistances between the sample and the electrodes. It is also hard to take a homogeneous, representative sample and to reproduce in the container the original compaction and moisture.

Four points with unequal spacing: Schlumberger-Palmer

In the Wenner array, the four probes are separated by a distance a. The guide points out two disadvantages. The voltage between the inner probes drops rapidly as the spacing increases, which used to exceed the sensitivity of instruments, although modern equipment mitigates this. And all four probes must be relocated for each depth.

In the Schlumberger-Palmer array the inner probes, separated by a distance d, stay together, and the outer ones are placed at a distance c from each of the inner ones. For each new depth only the outer probes are relocated. That makes it faster and useful when the current probes are far apart or when you want to measure with several positions of the current probe.

With the probes buried at a shallow depth compared with d and c, and with c greater than 2d, the apparent resistivity is:

ρ = π · c · (c + d) · R / d

where R is the ratio of the voltage measured between the inner probes to the current injected between the outer ones. It corresponds to equation (4) of the guide. The result is the apparent resistivity down to an approximate depth of (2c + d)/2, which is the distance from the center of the array to the outer current probes.

Depth variation (three-point)

The resistance of a vertical rod is measured repeatedly as it is driven deeper. With each increment, the test current passes through deeper soil, and the resistance reflects the apparent resistivity at that depth. The guide prefers rods for two reasons. Their theoretical resistance is easy to calculate with good accuracy. And driving them confirms how far one can go during installation. A disadvantage is that the rod can vibrate when driven and lose contact with the soil along its length, which makes conversion to apparent resistivity harder.

This method gives information about the soil near the rod, up to five to ten times its length. For large areas, several rod locations show whether there are lateral changes. If a large volume of soil is of interest, the guide considers the four-point method preferable, because driving very long rods is not always practical.

How the results are interpreted

Interpretation is, according to the guide, the hardest part of the measurement. Except in a few cases, a simple equivalent model of the soil has to be built. It depends on the accuracy and range of the measurements, the method used, the mathematical complexity accepted and the purpose. In electrical installations, the horizontal two-layer model is often accurate enough. There are also programs that fit multilayer models.

With depth variation, the curve of apparent resistivity against rod depth is compared with uniform or two-layer soil models. The guide shows a two-layer soil, with 300 Ω·m on top and 100 Ω·m below, where the curve starts near 300 Ω·m for rods of 0 to 6 m and approaches 100 Ω·m at greater depth. In the opposite case, with 100 Ω·m on top and 300 Ω·m below, the deep value cannot be read from the curve: you have to keep driving or apply an analytical fit.

With four points, the curve of apparent resistivity against spacing has a similar relationship with the structure of the soil. To estimate layer thickness there are empirical rules. The Gish and Rooney rule places a change of formation at a depth equal to the spacing at which the curve changes curvature. The Lancaster-Jones rule takes two thirds of the spacing at the inflection point. The guide illustrates them with a two-layer soil with a 6.1 m thick layer, and warns that none of those approximate rules predicted that depth. The apparent resistivity always changes to the right of the spacing that corresponds to the real change in the soil, and with an equal or smaller amplitude.

What probe spacing is needed

The effect of spacing on the accuracy of the soil model is summarized in Table 4 of the guide, taken from a study with perfect two-layer soils. With a spacing of 40 % of the grid length, the error in the grid resistance ranges from −50 % to +30 %. In step and touch voltages (as a percentage of GPR) it ranges from −20 % to +110 %. With 100 % of the length, from −33 % to +9 % and from −8 % to +50 %. With 300 %, from −17 % to +9 % and from −8 % to +20 %. The guide’s conclusion: spacings of the order of the grid dimension give enough accuracy for the voltages, but to estimate the resistance conservatively more than three times that dimension is needed.

Interference

Near the probes, metallic structures and circuits can falsify the reading. Passive interferences are metallic fences, pole grounds, large foundations, buried conductive objects and pipes. They act as short circuits that distort the soil potentials. Active ones are parallel transmission or distribution lines, parallel communication circuits and stray DC currents, which add to or subtract from the injected current. The guide asks for probes of a material that minimizes galvanic voltages, measuring on several profiles around the area, and repeating a measurement rotated by 90°: the values should be similar. The factors that change soil resistivity are explained in Soil Resistivity: Factors and Chemical Treatment. The resistivity of the yard’s gravel layer is measured with other procedures: see Substation Gravel Resistivity: How It Is Measured. If the soil model is used to calculate the grid resistance, why calculated and measured values differ explains the difference.

We measure your grounding system

At Tiza Group we measure soil resistivity with the method your site allows, in Colombia, or elsewhere on request, and interpret it for the grounding design. See the testing and commissioning service or write to us through contact. In the quotation we recommend the test and the equipment your case needs. For a first fit with your readings, the grounding resistance tool has a resistivity tab.

Related guides

• Soil Resistivity Measurement: Wenner Method
• Two-Layer Soil Model from Measurements
• Soil Resistivity: Factors and Chemical Treatment
• Substation Gravel Resistivity: How It Is Measured
• Ground Resistance Test: Fall-of-Potential and IEEE 81

References

• IEEE Std 81-2012, IEEE Guide for Measuring Earth Resistivity, Ground Impedance, and Earth Surface Potentials of a Grounding System: clauses 7.1 to 7.4 and Table 4; equations (3) and (4); Tables 3 and 4.
• IEEE Std 80, IEEE Guide for Safety in AC Substation Grounding.

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