Apparent Hysteresis in Archie’s Law: Implications of Changing Pore Fluid Conductivity for Electrical Resistivity Monitoring of Infiltration

Abstract

The electrical resistivity of the vadose zone is highly dependent on soil moisture content (VWC), making ERT a potential tool for non-intrusive infiltration monitoring. There’s a long history of using Archie’s law to convert resistivity values to VWC, often under the assumption that the pore-fluid conductivity is constant. Analysis of two years of soil conductivity and VWC data from sensors buried in a bioswale in Philadelphia, Pennsylvania showed that the characteristic curve of VWC versus resistivity exhibited hysteresis. The same value of resistivity was associated with different VWC during imbibition and drying. Accurate VWC could be estimated using Archie’s law only after incorporating changes in pore-fluid conductivity. Additionally, pore-fluid conductivity varied seasonally, with the highest values recorded during winter from road salt runoff. Archie exponents differed for sensors within 25 cm of each other despite both the uniform nature of the bioswale soil and fits to Archie’s Law for individual sensors, indicating considerable heterogeneity. This pattern was confirmed at two additional sites. Assuming the conductivity of the pore-fluid remains constant during infiltration not only produces erroneous soil moisture estimates, it can even reverse the apparent soil moisture trend. We conclude that to use ERT to monitor infiltration it is essential to independently record changes in pore-fluid conductivity, and that multiple sensors are required because changes in pore-fluid conductivity and Archie parameters can vary on a sub-meter scale for even apparently homogeneous sites. Additionally, long-term changes in Archie parameters, notably m, are possible, and may indicate long-term changes in soil fabric.