When you are engineering a high voltage substation or overhead line you need information about the local geo-electrical soil conditions. To measure the average resistivity of large volumes of undisturbed earth, a four-point method is often considered to be the best option.
There are multiple measurement setups that fall into this category, with the most famous ones being the Wenner method and Schlumberger method. For large electrode spacings a simplified formula can be applied, neglecting the depth of the electrodes in the earth. However, if the electrodes are placed closer to each other, the electrodes shall not be place to deep in order to measure accurately. In literature (IEEE Std.80) you can read about the depth not to exceed 10% of the electrode spacing, but how does this actually work?
Basic measurement description
Four-point measurements are based on the application of four electrodes that are placed in the earth. A current is injected in two of them and with the other two electrodes the soil potential is measured. Ohms law describes that voltage divided by current results in a resistance value, and this resistance value can be translated to a resistivity value for the soil, depending on the applied electrode configuration.
Now, the electrode configuration determines which area of the earth we are looking at. More specifically, the electrode spacing is related to the depth (or thickness) of the earth that is investigated. If the electrode spacing is varied, the area (width and depth) also changes. If multiple measurement values are collected they can be analysed in order to get to a soil model for the local situation. Examples for the Wenner method and Schlumberger method are presented in the animations below.
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Influence of the depth of the electrodes
We have performed some example calculations to show you what the influence of the depth of the electrodes is. For this, four electrodes are modelled in commercial software and the Wenner method is applied. A two-layer soil with arbitrarily chosen characteristics is applied. The top layer has a resistivity of 100 Ω.m and is 2 meters thick. The bottom layer has a soil resistivity of 200 Ω.m. The spacing is varied between 0.5 m and 30 m. The results are graphically presented in the figures below.
Apparent soil resistivity versus electrode spacing
The first picture shows the apparent soil resistivity per measurement. As you can see, all measurements show a slightly different curve. Most of them have a consistent pattern, however the values for spacings 0.5 m and 1 m in some cases seem to break this pattern.
Error per electrode depth
How much these curves deviate from the ‘perfect theoretical value’ is presented in the following graph. Errors of 10% to 20% can be seen for the deep electrodes, whereas the error for electrodes that are placed only 5 to 10 cm into the earth remains relatively low.
Error in percentage
If we relate the error to the depth of the electrode in relation to the electrode spacing (depth in percentage of spacing) we see the following trend, refer to the picture below. Basically they are the same curves as in the previous picture, but with a different relationship on the X-axis, so note that each curve starts at a different point (indicated with a dot). The red curve starting at the left represents the measurement with the electrode depth of 5 cm. This depth is at maximum 10% of the electrode spacing (at 0.5m) and the error for this measurement is at maximum around 1%. The other measurements go further to the right in the graph, up to 200% (since 1m depth is 200% of a spacing of 0.5m) and fall outside the graph in terms of error.
So this is how to place the electrodes
As shown in the picture above, as long as you measures with an electrode depth below 10% of the spacing, the error stays well below 2%, which is considered to be a very acceptable value. This is mainly important for the lower spacing distances. For large distances you may need to place the electrodes quite deep in order to be able to inject the current. Practical depths go up to 0.5 ~ 0.75 meters, since you may not be able to retrieve the electrodes after measurement without hurting your back.
For larger distances you may have another problem, being that the total resistance of the soil (mainly between the current electrodes) becomes too large. In that case, the current and/or soil potential values drop outside of the range of the measurement device. Instead of placing the current electrodes deeper you can consider to add extra electrodes here. Alternatively you can pour some (salt) water around the current electrodes.
If you want to know a bit more about spacing of the electrode, read this page too: https://www.allelectron.com/how-to-perform-a-wenner-measurement-efficiently/.