Laboratory study of the electrical properties of Lutetian limestones in the 100 Hz to 10 MHz frequency range

Abstract

Lutetian limestones have been widely used in historical monuments within the Paris Basin during the course of the medieval and modern periods. Among the physical properties that can be used to assess the evolution of the limestones in situ in the buildings and their present health, the complex effective permittivity in the 10–100 kHz frequency range is easy to measure and reflects the internal structure of the stone along with the dependence on the water content. To improve our knowledge about this property, a laboratory study on four samples collected in the relevant quarries has been undertaken using measurements in the 100 Hz–10 MHz frequency range. Except close to zero water content, the observed results exhibit a quasi‐absence of variation of the real effective permittivity with the water content. The frequency variation fits fairly well with a model taking into account a Jonscher's decrease, a direct current conductivity, a high‐frequency dielectric permittivity and losses, and a relaxation phenomenon. When fitted by a Cole–Cole model, the magnitude of the corresponding relative permittivity change always stays close to 30, but the time constant varies from 1.0 μs to 0.1 μs as the water content increases.

Experimental and numerical analysis of dielectric polarization effects in near‐surface earth materials in the 100 Hz–10 MHz frequency range: First interpretation paths

“…All the observations are correctly modelled and thus can be described by a continuous distribution of relaxations (Jonscher universal behaviour) followed, for low saturation materials, by one marked relaxation (Cole-Cole behaviour) that adds to the high frequency permittivity corresponding to the water molecule rotations. It is possible to compare the three criteria defined before to some already-published data, for example those of Souffaché and Tabbagh (2021) where one relaxation and its evolution with the sample water content and electrical conductivity is clearly identified. Criterion (1) is illustrated in Figure 9a by drawing in Log-Log the dependence of the time constant on the effective conductivity where, if the dependence is linear, the curve would be parallel to the second bisector line (decrease in power minus one).…”