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 ( λ sat ) increased with decreasing n (increasing compaction, 1 − n ). In addition, a declining λ sat ( T ) n =const trend was observed. The peak λ sat values and highest decreasing rate of λ sat 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 λ dry and λ sat data. The model by de Vries, with new fitted grain shape values, also closely followed measured λ sat 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 λ sat 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 λ sat as a product of thermal conductivity of the solid fraction (quartz plus other minerals) and a thermal conductance factor of water.