Analyse critique d'une methode d'estimation de la conductivite thermique d'un sol in situ

A numerical method for determining the thermal conductivity of a soil in situ is proposed. It requires the measure of the temperature at three levels in the soil. From the knowledge of the boundary conditions (temperatures at the top and the bottom of the soil layer) and an estimation of the initial the mal profile, the temperature at the intermediate level can be calculated by integration of the monodimensional heat conduction equation with a numerical method (finite elements method). The boundary conditions are interpolated by the FOURIER series. The heat capacity is calculated according to the model of DE VRIES. The thermal conductivity is estimated by minimizing the residual sum of squares between calculated and measured temperatures at the intermediate level. The soil layer can be considered either homogeneous or stratified in two sub-layers. Using simulated temperature data, the optimal conditions of use of the method are defined and the sensitivity of the method to errors made on the measure of the temperature and on the position of the temperature probes is studied.In the case of an homogeneous soil layer, the method yields a good estimation of the thermal conductivity (error ≤1%) with a 4 hours period of estimation, whatever the position of the intermediate probe. The more precise estimation is obtained with an intermediate probe placed at the middle of the layer and with a high thermal amplitude. The method is not sensitive to errors made on temperature measures (biased or truncated measures) if the estimation is made on a period of 24 hours. It is highly sensitive to errors made on the position of the temperature probes.In the case of a stratified layer, the method allows to estimate the thermal conductivity of each sub-layer whatever the position of the intermediate probe if the period of estimation is at least 12 hours. The method is very sensitive to errors made on temperature measures (whatever the duration of the estimation period), on the position of the temperature probes and on the position of the limit between the two sub-layers. Therefore, its use for a stratified soil layer seems delicate.