The Wenner four-probe method is commonly used for soil resistivity testing, where the standard apparent resistivity formula assumes point electrodes at the earth’s surface. In practice, bare rod stakes can be driven to non-negligible depths, and the point-source assumption basis of the Wenner apparent resistivity formula breaks down because current injection and voltage sensing occur along the entire rod length.
An engineer may opt to compensate for this error by using the apparent resistivity equation in IEEE 81 that compensates for probe depth, but this equation also has limitations due to the assumptions that govern it.
This paper will provide a comprehensive derivation of this probe depth compensation formula to provide the reader an understanding of its effect when used for computing a soil resistivity model. We investigate the error introduced when applying both the uncompensated and compensated formulas to realistic probe depths and spacings by simulating tests using a numerical software model. Results show that, for bare driven rods, the IEEE depth-compensation equation can overestimate apparent resistivity for small spacings, while the uncompensated equation underestimates it. An improved rule-of-thumb is proposed: applying the depth-compensation equation using an effective depth of approximately two-thirds of the driven depth reduces the modelling error for common test configurations.