The parameters used to describe the electrical conductivity of a porous
material can be used to describe also its thermal conductivity. A
new relationship is developed to connect the thermal conductivity
of an unsaturated porous material to the thermal conductivity of
the different phases of the composite, and two electrical parameters
called the first and second Archie's exponents. A good agreement
is obtained between the new model and thermal conductivity measurements
performed using packs of glass beads and core samples of the Callovo-Oxfordian
clay-rocks at different saturations of the water phase. We showed
that the three model parameters optimised to fit the new model against
experimental data (namely the thermal conductivity of the solid phase
and the two Archie's exponents) are consistent with independent estimates.
We also observed that the anisotropy of the effective thermal conductivity
of the Callovo-Oxfordian clay-rock was mainly due to the anisotropy
of the thermal conductivity of the solid phase.