Relationship between thermal conductivity and water content of soils using numerical modelling

There is no simple and general relationship between the thermal conductivity of a soil, λ, and its volumetric water content, θ, because the porosity, n, and the thermal conductivity of the solid fraction, λ s , play a major part. Experimental data including measurements of all the variables are scarce. Using a numerical modelling approach, we have shown that the microscopic arrangement of water influences the relation between A and 0. Simulated values for n ranging from 0.4 to 0.6, λ s ranging from 2 to 5 W m -1 K -1 and θ from 0.1 to 0.4 can be fitted by a simple linear formula that takes into account n, λ s and θ. The results given by this formula and by the quadratic parallel (QP) model widely used in physical property studies are in satisfactory agreement with published data both for saturated rocks and for unsaturated soils. Consequently, the linear formula and the QP model can be used as practical and efficient tools to investigate the effects of water content and porosity on the thermal conductivity of the soil and hence to optimize the design of thermal in situ techniques for monitoring water content.