Experimental Determination of TDR Calibration Relationship for Pyroclastic Ashes of Campania (Italy)

Abstract

Time domain reflectometry (TDR) is one of the most widely used techniques for indirect determination of soil volumetric water content (θ). TDR measures the relative dielectric constant (ε_r) which, in a three-phase system like the soil, depends on water, air, and solid matrix dielectric constants. Since dielectric constant of water is much larger than the other two, ε_r of bulk soil mainly depends on water content. In many cases, the application of TDR requires a specific calibration of the relationship θ(ε_r) to get quantitatively accurate estimates of soil water content. In fact, the relationship θ(ε_r) is influenced by various soil properties, such as clay content, organic matter content, bulk density, and aggregation. Numerous studies have shown that pyroclastic soils often exhibit a peculiar dielectric behavior. In Campania (Southern Italy) wide mountainous areas are covered by layered pyroclastic deposits of ashes (loamy sands) and pumices (sandy gravels), often involved in the triggering of landslides induced by rainwater infiltration. Reliable field measurements of water content of such soils are therefore important for the assessment of landslide risk. Hence, in this paper, the θ(ε_r) relationship has been experimentally determined on samples of typical pyroclastic soil of Campania, collected around Sarno, reconstituted with different porosities. The aim of the study is to identify specific calibration relationships for such soils based not only on empirical approaches. In this respect, a three-phase dielectric mixing model with a variable exponent is introduced, and the variable value of the exponent is related to the different dielectric properties of bond and free water within the soil pores.

Keywords: TDR calibration relationship; dielectric constant; pyroclastic soil; soil bulk density.

Figure 1

Sketch of the layered soil profile in the site of sample collection.

Figure 2

Particle size distribution curves of the three tested soils.

Figure 3

Experimental data of soil volumetric water content and relative dielectric permittivity compared with some empirical calibration curves from the literature. The best fitting third order polynomial of the experimental data is also plotted.

Figure 4

Experimental data for various porosities compared with calibration relationships from literature. (a) n = 0.5; (b) n = 0.55; (c) n = 0.6.

Figure 5

Fitting to the experimental data of the four-phase dielectric mixing model of Dasberg et al. [41], with calibrated parameters, for the various investigated porosities. (a) n = 0.5; (b) n = 0.55; (c) n = 0.6.

Figure 5

Fitting to the experimental data of the four-phase dielectric mixing model of Dasberg et al. [41], with calibrated parameters, for the various investigated porosities. (a) n = 0.5; (b) n = 0.55; (c) n = 0.6.

Figure 6

Experimental data at different porosities compared with the three-phase dielectric mixing model of Roth et al. [34] with various values of the exponent α. (a) n = 0.5; (b) n = 0.55; (c) n = 0.6.

Figure 6

Experimental data at different porosities compared with the three-phase dielectric mixing model of Roth et al. [34] with various values of the exponent α. (a) n = 0.5; (b) n = 0.55; (c) n = 0.6.

Figure 7

Values of the exponent α of the dielectric mixing model of Roth et al. [34] obtained, for all the experimental data, by forcing the model to give the same values of ε_r as those provided by the TDR measurements. The red curves are fitting expressions of the α(θ) trend.

Figure 8

Experimental data compared with calibration curves obtained with the dielectric mixing model of Roth et al. [34] with variable exponent α. Two different expressions of the α(θ) relationships are represented.