Thermal Conductivity of Standard Sands II. Saturated Conditions

A non-stationary thermal probe technique was used to measure the thermal conductivity of three saturated standard sands (Ottawa sand C-109, Ottawa sand C-190, and Toyoura sand) in a range of soil porosities (n) from 0.32 to 0.42, and temperatures (T) from 25 °C to 70 °C. The sand thermal conductivities at full saturation (λsat) increased with decreasing n (increasing compaction, 1 − n). In addition, a declining λsat(T)n=const trend was observed. The peak λsat values and highest decreasing rate of λsat with T were observed at the heaviest compaction and lowest tested T. This trend gradually diminished with increasing T and expanding volume of water (larger n) due to the markedly lower ability of water to conduct heat than quartz. A series-parallel model, containing three parallel paths of heat flow (through continuous solids, continuous fluid, and solids plus fluid in series), was successfully applied to predicted λdry and λsat data. The model by de Vries, with new fitted grain shape values, also closely followed measured λsat data. The corresponding square root of the relative mean squared errors varied from 2.9 % to 3.4 % for C-109, from 1.9 % to 3.0 % for C-190, and from 2.3 % to 2.4 % for Toyoura sand. The use of a weighted geometric mean model also provided good λsat estimates with errors ranging from 3.1 % to 3.5 % for C-109 and C-190 and 8.3 % for Toyoura sand. This paper also discusses a successful attempt to model λsat as a product of thermal conductivity of the solid fraction (quartz plus other minerals) and a thermal conductance factor of water.