We have developed a mechanistic model to interpret spectral induced
polarization data of partially saturated clay-rocks. This model accounts
for the polarization of the grains through an electrical double layer
model with a polarization model of the inner part of the electrical
double layer called the Stern layer. The polarization model accounts
also for the Maxwell-Wagner polarization at frequencies higher than
100 Hz. The Maxwell-Wagner polarization is modelled by using a conductivity
model modified to account for the presence of a non-wetting immiscible
phase like air in the pore space. The resulting model is consistent
with the first and second Archie's laws in the case where surface
conductivity can be neglected. The volumetric charge density of the
diffuse layer at saturation is divided by the saturation of the water
phase to account for the partial water saturation of the porous material.
The model comprises seven fundamental parameters: the formation factor,
the second Archie's exponent, a critical water saturation level,
the mean electrical potential of the pore space at saturation, the
density of the counterions in the Stern layer, and at least two parameters
describing the grain size distribution. Most of these parameters
can be derived independently using alternative measurements and electrochemical
models. Measurements were performed in the frequency range 10 mHz-45
kHz using five samples from the Callovo-Oxfordian formation in the
eastern part of the Paris Basin, France. The model agrees fairly
well with the experimental data at saturation and for partially saturated
clay-rocks down to 1 Hz. Most of the seven physical parameters entering
the model were independently evaluated.