A resistivity survey produces a table of readings at different electrode spacings. A grid design calculation needs a description of the soil. Soil resistivity modelling is the step between them, and it is the step where the value of the survey is either realised or lost.

The modelling is a fitting exercise: find the layered structure whose calculated response reproduces the measured values. When the fit is good and the measurements span the right range, the resulting model is a usable design input. When it is not, the designer is working from numbers whose relationship to the site is uncertain.

From survey data to a soil model

Each measurement gives an apparent resistivity at a specific electrode spacing. The apparent value is a weighted average of the true resistivities of the material the current has passed through, weighted by the geometry of the electrode array and the distribution of current with depth.

The model is found by calculating what the apparent resistivity would be for a proposed layered structure at each of the measured spacings and adjusting the layer parameters until the calculated values match the measured ones. The result is a set of layer resistivities, thicknesses and, where the deepest layer is treated as extending to infinity, a description of the soil that the grid calculation can use.

The fitting is mathematically well defined but not unique. Different combinations of layers can produce similar apparent resistivity curves, particularly when the resistivity contrast between layers is modest, and the ambiguity has to be recognised rather than hidden.

Why a single measurement is not enough

A single measurement at one spacing produces one apparent resistivity, which could be produced by any number of layered structures. Reducing the whole survey to that number discards the depth information the designer needs.

The practical consequence shows up in the design. A site with a resistive surface layer over a conductive stratum behaves very differently, for grid purposes, from a site with the reverse arrangement, and both can produce a similar average value. The grid design that suits one is inefficient or inadequate for the other.

The number of spacings needed depends on the site. A simple two-layer structure can be resolved from a modest number of well-chosen spacings; a site with three or more layers or with lateral variation needs more, and no amount of measurement resolves a structure that the spacing range cannot see.

Layered soil and equivalent models

Increasing the number of layers improves the fit but not necessarily the model. Beyond a point the additional layers are fitting the uncertainty in the measurements rather than describing the site, and a model with more layers than the data supports gives a false impression of precision.

Choosing spacing for the depth of interest

The spacing range should be set by what the design needs to know. The surface layer governs the surface potentials, so the small spacings matter for the touch and step potential calculation. The deeper material governs the grid resistance, so the large spacings matter for that.

A practical rule is to span from a fraction of the grid dimensions to several times them. The smallest spacing should be small enough to resolve the surface layer thickness, and the largest should be comparable to or larger than the overall dimensions of the proposed grid.

Where the grid is large, the largest spacing can be substantial, and the survey layout becomes a practical exercise in finding straight, clear ground. Where the site is constrained, alternative array geometries are used, and the interpretation has to account for the geometry used because the relationship between spacing and depth differs.

Feeding the grounding grid design

The designer uses the model to calculate the grid resistance for a proposed geometry and to calculate the surface potentials under fault current. The grid can then be adjusted within the model: conductors added, depth changed, the layout extended beyond the fence, or deep electrodes added where the model shows a conductive layer at depth.

Which of those adjustments is effective depends entirely on the model. A site where resistivity falls with depth can be improved substantially by driving electrodes into the lower layer; a site where it rises with depth cannot. Without the model, the designer cannot tell which situation applies and may apply the wrong measure.

The designer also needs the fault current the installation will see, the clearing time and the surface layer treatment that is proposed, because those quantities enter the same calculation. The resistivity model is one input among several, and it is the one that describes the site.

Verifying the model after installation

The model can be tested against the installed grid by measuring the grid resistance after construction and comparing it with the value the model predicted for the as-built geometry. Agreement supports the model; a consistent disagreement indicates that the model or the as-built record is wrong.

The comparison is only meaningful where the installation corresponds to the design. Where the grid was modified during construction, the calculation has to be revisited with the installed geometry before the comparison can say anything about the model.

The measurement conditions also matter. Soil resistivity varies with moisture and temperature, so a post-construction measurement taken in different conditions from the survey will differ from the prediction for that reason alone. Recording the conditions for both is what allows the comparison to be interpreted.

Common handoff errors

The first is handing over the apparent resistivity values without the spacings, or the spacings without the array geometry. The values cannot be interpreted without knowing how they were obtained.

The second is handing over a single number as the site resistivity. It discards the depth information and forces the designer to assume a structure, which is the opposite of what the survey was for.

The third is omitting the conditions. A survey taken in dry conditions and a survey taken in wet ones produce different values, and a model without its conditions cannot be compared with a later measurement or adjusted for season.

The fourth is omitting the locations of the measurement points. Where the survey covered only part of the site, or where different areas gave different results, the model’s area of applicability has to be stated. A model applied uniformly across a site where it does not hold is a source of design error that no later measurement will reveal.

Documentation the designer must retain

The designer should retain the apparent resistivity values with their spacings and locations, the array geometry used, the conditions at the time of measurement, the fitted layer model with its parameters, a statement of the fit quality and any ambiguity, and the method used to derive the model.

That package is what allows the design to be revisited later. When the site changes, or when a new installation is proposed nearby, or when the grid has to be extended, the original model is the starting point, and a model whose derivation is unknown cannot be extended with confidence.

The package also belongs in the safety compliance record, because the design calculation that established the surface potentials rests on it. The earthing requirements for high-voltage installations are set out in IEC 61936-1 and the low-voltage framework in IEC 60364-1; instrument method documentation describing the four-electrode arrangement and its interpretation is published by suppliers such as Fluke and Hioki; substation earthing design practice is coordinated through CIGRE study committees and published by EPRI; and the instrument range is grouped on the electrical resistance testing hub.

The survey procedure that produces the raw data this modelling step consumes is covered in the existing article on performing a soil resistivity test for substation grounding grid design.