Soil resistivity

The Wenner four-pin method, as shown in figure above, is the most commonly used technique for soil resistivity measurements.[4][5][6][7] Using the Wenner method, the apparent soil resistivity value is:

${\displaystyle \rho _{E}={\frac {4\cdot {\pi }\cdot a\cdot R_{W}}{1+{\frac {2\cdot a}{\sqrt {a^{2}+4\cdot b^{2}}}}-{\frac {a}{\sqrt {a^{2}+b^{2}}}}}}\,}$ [8]

where

ρ_E = measured apparent soil resistivity (Ωm)

a = electrode spacing (m)

b = depth of the electrodes (m)

R_W = Wenner resistance measured as "V/I" in Figure (Ω) If b is small compared to a, as is the case of probes penetrating the ground only for a short distance (as normally happens), the previous equation can be reduced to:

${\displaystyle \rho _{E}=2\cdot \pi \cdot a\cdot R_{W}\,}$[8]

In the Schlumberger method[4][6][7] the distance between the voltages probe is a and the distances from voltages probe and currents probe are c (see figure above).

Using the Schlumberger method, if b is small compared to a and c, and c>2a, the apparent soil resistivity value is:

${\displaystyle \rho _{E}={\pi }{\frac {c\cdot (c+a)}{a}}R_{S}\,}$

where

ρ_E = measured apparent soil resistance (Ωm)

a = electrode spacing (m)

b = depth of the electrodes (m)

c = electrode spacing (m)

R_S = Schlumberger resistance measured as "V/I" in Figure (Ω)

Measured volume

The conversion between values measured using the Schlumberger and Wenner methods is possible only in an approximate way.[7] In any cases, for both Wenner and Schlumberger methods the electrode spacing between the currents probe corresponds to the depth of soil investigation and the measured apparent soil resistivity is referred to a soil volume as in the figure.

The current tends to flow near the surface for small probe spacing, whereas more current penetrates deeper into the soil for large spacing. The resistivity measured for a given current probe spacing represents, to a first approximation, the apparent resistivity of the soil to a depth equal to that spacing.

If the apparent soil resistivity measured with Schlumberger method ρ_E (with the corresponding electrode spacing a_S and c) is given, assuming that the soil resistivity refers to a volume as in the figure with a=L/3 follows:

${\displaystyle R_{W}={\frac {\rho _{E}}{2\cdot \pi \cdot a_{W}}}\,}$

with

${\displaystyle a_{W}={\frac {a_{S}+2c}{3}}\,}$

where:

R_W = equivalent Wenner resistance (Ω)

a_W = equivalent electrode spacing with Wenner method (m)

a_S = electrode spacing between voltages probe with Schlumberger method (m)

c = electrode spacing between voltages and currents probe with Schlumberger method (m)

If the measured Schlumberger resistance is given, before calculating the apparent soil resistivity the following factor must be calculated:

${\displaystyle \rho _{E}={\pi }{\frac {c\cdot (c+a_{S})}{a_{S}}}R_{S}\,}$

The Wenner method is the most widely used method for measuring soil resistivity for electrical grounding (earthing) purposes. The Schlumberger method was developed to increase the voltage signal for the earlier, less sensitive instruments, by placing the potential probes closer to the current probes.

The soil resistivity measurements will be affected by existing nearby grounded electrodes. Buried conductive objects in contact with the soil can invalidate readings made by the methods described if they are close enough to alter the test current flow pattern. This is particularly true for large or long objects.