Thermal Conductivity of Standard Sands. Part III. Full Range of Saturation

Abstract

The thermal conductivity $(\lambda )$ of three unsaturated standard quartz sands (Ottawa C-109 and C-190, and Toyoura) was measured by a transient thermal-conductivity probe, at room temperature of approximately $25\,^{\circ }\text{ C }$ and at loose and tight compactions. The measurements were carried out at different degrees of saturation $(S_\mathrm{r})$ from dryness to full saturation. In general, a sharp $\lambda$ increase was observed at low $S_\mathrm{r}$, followed by a moderate rise until full saturation. However, experiments on loosely compacted C-190 samples revealed $\lambda$ deviation from a general trend ($\lambda$ vs $S_\mathrm{r})$ caused by water percolation. Alternatively, successful experiments were carried out on loosely packed unsaturated C-190 samples using 1 % agar gel. For loosely compacted C-109 and Toyoura, $\lambda$ data obtained from 1 % agar gel closely agreed with $\lambda$ data for water as a saturation medium. The measured data were used to verify a model by de Vries for unsaturated soils. The model largely underestimates experimental data at $S_\mathrm{r}<0.5$ and produces an overall root-mean-square error of about $0.2\, \text{ W }~{\cdot }~\text{ m }^{-1}~{\cdot }~\text{ K }^{-1}$. Measured $\lambda$ data agreed with data by a steady-state technique (a guarded hot-plate apparatus) at dryness and full saturation and exceeded the steady-state data in the unsaturated region. However, TCP data can be considered more reliable due to a lower temperature increase during $\lambda$ measurements and a shorter testing time. Consequently, in the case of unsaturated soils, evaporation and migration of water and steam can be avoided.

Appendix

See Tables 5, 6, and 7.

Table 5 C-109: thermal-conductivity data and RMSE ($\text{ W }~{\cdot }~\text{ m }^{-1}~{\cdot }~\text{ K }^{-1}$) evaluation

Table 6 C-190: thermal-conductivity data and RMSE ($\text{ W }~{\cdot }~\text{ m }^{-1}~{\cdot }~ \text{ K }^{-1}$) evaluation

Table 7 Toyoura sand (TS): thermal-conductivity data and RMSE ($\text{ W }~{\cdot }~\text{ m }^{-1}~{\cdot }~\text{ K }^{-1}$) evaluation