Two-layer soil

A two-layer soil model describes the ground as an upper layer of resistivity ${\rho }_1$ and depth $h$ over a lower layer of resistivity ${\rho }_2$. IS 3043:1987 notes that a gradual variation or a two-layer model may be adopted when the soil is not uniform (§36.1.1).

Read first: Soil resistivity and Wenner readings

1Readings that vary with spacingCopy link to Readings that vary with spacing

A Wenner reading at a small spacing reflects the soil near the surface, and one at a large spacing the soil deeper down (Soil resistivity and Wenner readings). IS 3043:1987 asks for a curve of resistivity against spacing in that case, analysed into layers (§36.5.1).

2The apparent resistivity of two layersCopy link to The apparent resistivity of two layers

The current of the outer electrodes spreads into both layers, and the interface reflects part of it. The apparent resistivity a Wenner reading gives over two layers is a series of these reflections, each weighted by a power of the reflection factor $K$.

$K$ lies between −1 and 1. It is negative when the lower layer's resistivity is below the upper's, and positive when it is above. At a small spacing the terms of the series vanish and ${\rho }_a$ tends to ${\rho }_1$. With a negative $K$ the terms lower ${\rho }_a$ as the spacing grows, so readings that fall with spacing describe a lower layer of lower resistivity.

3Fitting the layersCopy link to Fitting the layers

The design service finds the ${\rho }_1$, ${\rho }_2$ and $h$ whose apparent resistivities by Eq. (1) are nearest the readings. It minimises the squared relative differences, the objective of Dautbašić and Dujak (Eq. 4), on the logarithms of the three unknowns, starting from the best point of a coarse grid. A fit needs readings at three or more spacings, one for each unknown. With fewer, the design takes the Wenner average.

A fit with a relative error above 10 % is not taken, and the design takes the Wenner average. Layers whose reflection factor is within ±0.05 are taken as one soil. Figure 1 shows the readings of Soil resistivity and Wenner readings, Example 1 and the fitted curve.

4How the design uses the layersCopy link to How the design uses the layers

The design multiplies both layers by the season factor. In a two-layer soil the numerical analysis of the earth mat gives the verdict, since it takes the layers, within the size of mat it takes (Earth mat analysis in two-layer soil, The voltages on the surface). The surface layer's derating factor takes the upper layer's resistivity. The IEEE 80-2013 equations, which take one resistivity, are calculated beside it with the Wenner average and the season factor.