Technical Article

# Measuring Soil Resistivity With the Wenner Method

September 01, 2020 by Lorenzo Mari

## Learn how to measure soil resistivity with the Wenner Method.

Resistivity estimates based on soil classification are a crude approximation of their actual value. This is why on-site measurements are crucial to designing with reliable figures.

Conventional laboratory experimental testing is costly and takes a long time when dealing with a large number of soil samples. Electrical measurements on-site are inexpensive, swift, reliable, and non-destructive.

There are several approaches to measure soil resistivity. Two of them are particularly popular: the Schlumberger method and the Wenner method. Both ways use four electrodes, two to inject current, and two to measure potential.

The Schlumberger method changes the distance between the electrodes. In the Wenner method, the electrodes are equally spaced. This digest will emphasize Wenner’s approach, developed by Dr. Frank Wenner in 1915, because it is widely accepted in the field.

Figure 1 shows the Wenner method pattern, frequently named the “four-terminal method.” This term may be ambiguous as the Schlumberger method also uses four terminals.

##### Figure 1 Wenner set-up (No scale)

A current I, injected into the ground through a small electrode (1), returns through another small electrode located a long distance away (4). Two additional electrodes, (2 and 3), also small, display electric potentials (V1 and V2) referred to a very distant point, ideally infinity. These four equidistant electrodes are in a straight line.

The estimation of soil resistivity requires the measurement of the injected current and the difference in potential between electrodes 2 and 3 (V = V1 – V2). The soil resistivity is

$$\rho=\frac{4\pi aR}{1+\frac{2a}{\sqrt{a^2+4h^2}}-\frac{a}{\sqrt{a^2+h^2}}}$$

where,

⍴ = soil resistivity

R = V/I

a = electrode spacing

h = depth

If the depth is much less than the electrode spacing (h ≤ 0.1 a), then

$$\rho=2\pi aR$$

The depth of the computed resistivity is a, i.e., the same as the spacing between electrodes.

These measurements can be made with DC or AC at different frequencies, usually from 40 Hz to 100 Hz. Some unique measurements use frequencies above 100 Hz. Using 50 Hz or 60 Hz may produce measurement errors due to stray currents at these frequencies. DC may have a polarizing effect on the salts found in the soil.

When the soil is homogeneous, the resistivity value measured for a first electrode location should give the same result as for a second electrode location. For example, if we measure a = 5 m, the result should be the same for values, say a = 10 m or a = 20 m. However, as mentioned in the previous article, homogeneous soil is extremely rare.

## Apparent Resistivity Curves

A practical way of analyzing the data is to draw up a resistivity field curve as a function of depth a, in several directions. This way gives us an idea of how resistivity changes both in depth and sideways. When making measurements in several directions, keep the same point of origin to ensure consistent results.

When the soil is heterogeneous, the resistivity varies for different electrode positions. These resistivity values are known as apparent resistivity a. The plot of apparent resistivity as a function of depth is the basis to interpret the results and develop a stratified model for the soil under study.

Figure 2 shows some examples of apparent resistivity curves. These are typically log-log plots.

##### Figure 2 Apparent resistivity curves

There is no fixed rule for interpreting the results and obtaining a soil model. But it can be concluded, from inspection, if the terrain is homogeneous or heterogeneous, requiring a model with several layers. There are computer programs accessible to obtain two-layer and multi-layer soil models.

From figure 2, it is possible to estimate the first number of layers of the model. Curve 1 shows an apparent resistivity with minimal variations, so an assumption of homogeneous soil is in order. For curves 2 and 4, a two-layer model will do. Two-layer models generally give good results. Curve 3 requires a multi-layer model.

## An Example

Find the soil resistivity with four electrodes evenly spaced (Wenner set-up), as shown in Figure 3, with a = 20 m = 2,000 cm

##### Figure 3 Example with Wenner Method

Condition h ≤ 0.1 a  satisfied with h = 1.5 m = 150 cm

Apply a voltage between electrodes 1 and 4 to generate a current of 1 A

The voltage drop measured between electrodes 2 and 3, is 2V

R = V/I = 2V/1A = 2 Ω

⍴ = 2πaR ≈ 2·3.14 ·2,000 cm · 2Ω = 25,120 Ω·cm

This resistivity figure is the average to a depth of 20 m.

Make several measurements, using the same procedure, for different values of electrode spacing, plot the apparent resistivity diagram, and choose a suitable soil model.

## A Review of Measuring with the Wenner Method

Resistivity values may be computed by field and laboratory electrical measurements.

Lab studies are expensive and sometimes slow. On-site measurements are faster, more practical, and reliable.

There are several approaches for measuring soil resistivity on site. Of these, the most widely used is the Wenner or four-terminal method.

Plot the figures acquired by the Wenner method to set up the apparent resistivity curves, and choose a suitable soil model. 