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Wenner method for concrete and soil conductivity measurements

Wenner electrode array is an assembly of four collinear and equally spaced electrodes where the current is supplied through two outer electrodes and the potential is measured at two inner electrodes. Electrodes are attached to the surface of some solid media or specimen (soil, concrete) and the resistivity of the bulk material is measured this way. Wenner method measurements are performed for electrical soil testing, analysis of the concrete structure and widely used in geophysics, non-destructing evaluation of the building structures. Electrical grounding calculations and many other applications.

Problem Type:
A 3D extrusion problem of DC conduction.

Geometry:
Electrical resistivity of concrete Wenner array is used to measure electrical surface resistivity of concrete specimen. Concrete A M N B a a a V I

Given:
Electric conductivity of concrete σ = 0.01 S/m;
Electrodes spacing a = 38 mm (1.5");
Injected current I = 50 uA;

Task:
Calculate the electric potential drop on Wenner array electrodes.

Solution:
Wenner method is based on following equation
ρ = 2π*a * (V / I)
where ρ is bulk material electrical resistivity (reciprocal to electrical conductivity σ),
I is injected current and V is a measured voltage.

Results:
Wenner method formula gives V = ρ * I / (2π*a) = (1/0.01) * 50e-6 / (2*3.142*0.038) = 0.0209 V.

QuickField simulation gives:
* potential on electrode M is VM = 0.204 V.
* potential on electrode N is VN = 0.183 V.

Simulated potential difference is VM - VN = 0.204-0.183 = 0.0210 V

Electric potential distribution in the concrete specimen during Wenner probe resistivity measurements.

Electrical resistivity of concrete

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