Quantitative Relationship Between Electrical Resistivity and Water Content in Unsaturated Loess: Theoretical Model and ERT Imaging Verification

As a typical porous medium, unsaturated loess demonstrates critical hydro-mechanical coupling properties that fundamentally influence geohazard mitigation, groundwater resource evaluation, and foundation stability in geotechnical engineering. This investigation develops a novel theoretical framework to overcome the limitations of existing models in converting electrical resistivity tomography (ERT) profiles into water content distributions for unsaturated loess through quantitative inversion modeling. Systematic laboratory investigations on remolded loess specimens with controlled density and water content conditions revealed distinct resistivity–water interaction mechanisms. A characteristic two-stage decay pattern was identified: resistivity exhibited an exponential decrease from 420 Ω·m (water saturation (Sw = 10%)) to 90 Ω·m (Sw = 40%), followed by asymptotic stabilization at Sw ≥ 40%. The derived quantitative correlation provides a robust mathematical basis for water content profile inversion. Field validation through integrated ERT and borehole data demonstrated exceptional predictive accuracy in shallow strata (<20 m depth), achieving mean absolute errors of <5%. However, inversion reliability decreased with depth (>20 m), primarily attributed to density-dependent charge transport mechanisms. This underscores the necessity of incorporating coupled thermo-hydro-mechanical processes for deep-layer characterization. This study provides a robust framework for engineering applications of ERT in loess terrains, offering significant advancements in geotechnical monitoring and geohazard prevention.