Canadian Field Soils III. Thermal-Conductivity Data and Modeling

Abstract

Forty field soil samples, from nine Canadian Provinces, were laboratory tested for their ability to conduct heat, i.e., thermal conductivity ($\lambda$), using a non-stationary probe technique. The measurements were carried out on moderately compacted samples at room temperature, and over a full range of degree of saturation ($S_{\mathrm{r}})$ ranging from dryness to full saturation. The analysis of $\lambda$ data revealed a strong nonlinear variation of $\lambda$ versus $S_{\mathrm{r}}$ that can be sub-analyzed in four $S_{\mathrm{r}}$-based domains, i.e., residual, transitory meniscus, micro/macro-porous capillary, and superfluous. In the residual domain ($0 < S_{\mathrm{r}}< S_{{\hbox {r-cr}}})$, a very small $\lambda$ variation is observed. In the transitory meniscus domain ($S_{{\hbox {r-cr}}} < S_{\mathrm{r}} < S_{{\hbox {r-}\mathrm{PWP}}})$, for the majority of soils, a sharp $\lambda$ increase was observed. In the micro/macro-porous capillary domain ($S_{{\hbox {r-}\mathrm{PWP}}} < S_{\mathrm{r}} < S_{{\hbox {r-}\mathrm{FC}}})$, a moderate $\lambda$ increase was noted. Finally, in the superfluous domain ($S_{{\hbox {r-}\mathrm{FC}}} < S_{\mathrm{r}} < S_{{\hbox {r-sat}}})$, a very slight $\lambda$ increase was generally noted. On average, the highest $\lambda$ values (from 1.9 $\hbox {W}{\cdot }\hbox {m}^{-1}{\cdot } \hbox {K}^{-1}$ to 3.2 $\hbox {W} {\cdot }\hbox {m}^{-1}{\cdot } \hbox {K}^{-1})$ were obtained from saturated soil samples with high quartz content, e.g., samples from sites in Nova Scotia and Prince Edward Island. On the other hand, the lowest $\lambda$ (from 1.1 $\hbox {W}{\cdot }\hbox {m}^{-1}{\cdot }\hbox {K}^{-1}$ to 1.4 $\hbox {W}{\cdot }\hbox {m}^{-1}{\cdot }\hbox {K}^{-1})$ was observed from saturated soil samples with lower quartz content, e.g., British Columbia samples. The measured data were used to verify a recently developed series–parallel (S–${\vert }{\vert }$) model for unsaturated soils. On average, estimates of the S–${\vert }{\vert }$ model, with a parallel arrangement of air and water in the third of three conductive paths, were within ${\pm }0.08\,\hbox {W}{\cdot }\hbox {m}^{-1}{\cdot }\hbox {K}^{-1}$ of experimental data. However, the S–${\vert }{\vert }$ model, with a series arrangement of air and water in the third conductive path, showed slightly better estimates when it was applied to fine-textured soils. In addition, there was no strong correlation noted between the performance of the S–${\vert }{\vert }$ models and soil quartz content. Consequently, it is recommended to compare estimates from both models when they are applied to experimental data.

Appendices

Appendix 1

See Tables 8, 9, 10, 11, 12, 13, 14, 15, and 16.

Table 8 Soils from Nova Scotia

Table 9 Soils from Prince Edward Island

Table 10 Soils from New Brunswick

Table 11 Soils from Quebec

Table 12 Soils from Ontario

Table 13 Soils from Manitoba

Table 14 Soils from Saskatchewan

Table 15 Soils from Alberta

Table 16 Soils from British Colombia

Appendix 2

See Table 17.

Table 17 Canadian soils: mineral content

Appendix 3

See Table 18.

Table 18 Thermal-conductivity data ($\hbox {W} {\cdot } \hbox {m}^{-1} {\cdot } \hbox {K}^{-1}$) of 40 Canadian soils and their relative standard deviations (%)

Appendix 4

Forty Canadian soils: thermal conductivity versus degree of saturation (Figs. 15, 16, 17, 18, 19, 20, 21, 22).

Fig. 15

Nova Scotia soils: thermal conductivity versus degree of saturation

Fig. 16

Prince Edward Island soils: thermal conductivity versus degree of saturation

Fig. 17

New Brunswick soils: thermal conductivity versus degree of saturation

Fig. 18

Quebec soils: thermal conductivity versus degree of saturation

Fig. 19

Ontario soils: thermal conductivity versus degree of saturation

Fig. 20

Manitoba soils: thermal conductivity versus degree of saturation

Fig. 21

Alberta and Saskatchewan soils: thermal conductivity versus degree of saturation

Fig. 22

British Columbia soils: thermal conductivity versus degree of saturation