Multilayer soil resistivity modelling for earthing designs

We have developed an accurate automatic algorithm for determining multilayer soil resistivity models from soil resistivity measurements data for use in earthing systems modelling.

This new algorithm is incorporated into SafeGrid Earthing Software?.

Effects of soil resistivity on earthing systems

Soil electrical resistivity has a large impact on earthing system performance. The actual soil resistivity profile of the soil affects the grid resistance, Grid Potential Rise (GPR) as well as the distribution of leakage currents from a buried grid during a fault into the surrounding soil. The behaviour of the fault currents which flow in the soil layers in turn affects the resultant touch and step voltages.

Let’s examine the behaviour of leakage currents for simple two-layer soil examples – however it should be noted the majority of real soil resistivity structures are multi-layered. For a high-on-low soil resistivity model the fault current which enters the top layer of high resistivity layer wants to escape into the bottom layer of low resistivity (refer to the first two plots below). On the other hand, for a low-on-high situation the larger resistivity of bottom-layer soil impedes current flowing into the deep soil layers causing surface voltages to increase (refer to the second two plots below).

The bottom layer resistivity will have the most influence on the grid resistance and grid potential rise compared with the top layer (due to their relative thicknesses – the bottom layer thickness extends to infinite depth).?Therefore, a low resistivity bottom layer will result in low overall grid resistance and GPR – this is the advantage.?However, if the soil resistivity model is high-on-low then the touch voltages may be much greater than for low-on-high due to the steep variations in the surface voltages profile.

Guide to soil resistivity measurements

Soil resistivity measurement tests are imperative and should be taken at several places within or nearby to the site. Several different measurement techniques are described by the IEEE Standard 81 however the Wenner four-pin method is the most used. Field measurements are taken along several profiles at or near to the project site to detect lateral changes in resistivity and possible interference effects due to buried conductive objects.

Measurement records should include temperature data and information on the moisture content of the soil at the time of measurement. All data available on known buried conductive objects in the area studied should also be recorded. It is important to perform field measurements during adverse weather conditions to obtain conservative values during summer or winter time (especially if the earth freezes).

The number of measurements should be greater where the variations in soil resistivity are large (i.e. for multi-layered soils). To have a good indication of the resistivity of the bottom soil layers it is important to have measurements at spacings of at least the diagonal diameter of the earthing system being designed.

Interpreting the soil model from measurements

Interpretation of the apparent resistivity measurements is usually a difficult task. The basic objective is to derive a soil model which is a good approximation of the actual soil, but a perfect match is not likely. Most soil electrical resistivity structures are multi-layered and heterogenous.

Below is an image of an apparent resistivity plot taken from IEEE Standard 80 which depicts 3 distinct resistivity layers. Equivalent two-layer soil models can be done manually. However, software applications which create multilayer soil models from measurements are the most accurate.

There is an extensive level of engineering judgement and prudence required in acquiring resistivity test data. There are no simple rules-of-thumb as to what extent is required to accurately evaluate and develop representative soil models for use in earthing analysis. [CIGRE TB 749]

Automatic software algorithm for multi-layered soils

We have developed a software algorithm which automatically obtains horizontally stratified multilayer soil models from field measurements.

The user enters field measurements which are plotted, and user specifies the number of layers. Apparent resistivity is numerically calculated and then an optimisation algorithm is used to match the model parameters with the field measurements.

Below are several real-world soil measurement datasets with fitted multilayer soil models.

The Root Mean Squared Error (RMSE) is a measure of how well the numerically calculated multilayer model fits with the measured data. In general, we say a model with RMSE ≤ 15 % has a good fit with the field data.

In the plots you will noticed we have included the models derived using SafeGrid and also using CDEGS software with the RMSE shown for the models.