Schlumberger array - QuickField simulation example
Apparent soil resistivity measured with a Schlumberger electrode array in homogeneous and multilayer ground, including the effect of electrode spacing.
How to calculate apparent soil resistivity in homogeneous and layered ground using a Schlumberger electrode array?
Answer Typical applications Geometry
Given
Task
Solution
The electrode diameter is small compared to the distances between electrodes so the electrode is modelled as an edge. Electric potentials ±10 V are specified on current probe electrodes. QuickFied calculates current density and potential distribution in the soil.
Geometry model features symmetry so we reduce the simulation domain. Remember to take this fact into account when computing currents and voltages.
Results
Reference
First we test the Schlumberger array method with the homogeneous soil model with the resistivity of 100 Ohm*m. This way we will be able to compare the actual soil resistivity value with the value calculated by the Schlumberger array method.
Then we change the soil resistivity to a three layered model and run the analysis again.
Engineering question
Calculate electrode current and measured voltage in a 3D conduction model, then apply the Schlumberger geometric factor to obtain apparent resistivity.
Schlumberger electrode arrays, soil resistivity surveys, geophysical resistivity sounding
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Simulation problem
Problem Type
3D problem of DC conduction.
Probe electrodes spacing is a = 40 cm. Distance from the voltage probe to the current probe electrodes is c = 130 cm. Electrodes are buried into the ground by b = 5 cm.
Calculate the soil resistivity using the Schlumberger array.
The Schlumberger array* method uses the following equation to calculate soil resistivity:
ρ = (ΔV / I) * π* c * (c + a) / a
where I is the current injected by the current probe electrodes V+ and V-);
ΔV = V2 - V1 is a voltage drop between voltage probe electrodes.
Current probe electrode I Voltage probe electrode ΔV Calculated resistivity
by the Schlumberger array method
Homogeneous soil
ρ=100 Ohm*m2*0.00400 A 2*0.0232 V 100.7 Ohm*m
Three layered soil
ρ1=100 Ohm*m
ρ2=80 Ohm*m
ρ3=25 Ohm*m
2*0.00402 A 2*0.0176 V 76 Ohm*m
*Wikipedia Soil resistivity, Schlumberger method.
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