Thermophysical model for determining the thermal conductivity coefficient of soil by a cone probe of constant heating power

Introduction. The thermophysical properties of soil can be determined in laboratory and field conditions. Field methods are more accurate because they are performed with minimal disturbance to the natural structure and thermal and moisture conditions of the soil. The most common are probe methods based on the introduction of a heat source into the soil and the measurement of the adjacent soil temperature over time using a temperature sensor installed in the probe. One of the most promising areas for developing methods for determining the thermophysical properties of permafrost and thawed soils is the use of the thermostatic probe method (HT-CPT)  – static probing using probes equipped with a heating device and a temperature sensor. This issue requires a comprehensive study, primarily the development of a thermophysical model for the interaction of a cone probe with constant heating power with the soil.

Aim. Development of a thermophysical model for determining the thermal conductivity coefficient of soil using a cone probe with constant heating power.

Materials and methods. The analytical thermophysical model was developed taking into account the fundamental principles of heat transfer theory. The following calculation assumptions were adopted in developing the model: the soil’s thermophysical properties are isotropic and constant; there are no phase transitions in the soil upon heating; the soil’s thermophysical properties do not change; the cone heats uniformly, etc.

Results. An analytical model was developed that allows one to determine the thermal conductivity of soil using a cone probe with constant heating power. The results of numerical and flume experiments confirmed the validity and applicability of the developed analytical model for determining the thermal conductivity of frozen soil during thermostatic probing with an HT-CPT probe.

Conclusions. Based on an analysis of the thermophysical interaction between a cone probe generating a low-power heat flux and thawed and frozen (without thawing) soil, an analytical solution was obtained that allows one to determine the soil’s thermal conductivity from the cone heating thermogram and the probe’s thermal coefficient.

1. Andersland O.B. Frozen Ground Engineering / O.B. Andersland & B. Ladanyi. ASCE. John Wiley & Sons, Inc., Hoboken, New Jersey. 2004. 363 p.

2. Blackwel J.H. A transient-flow method for determination of thermal constants of insulating materials in bulk. Journal of Applied Physics, 1954, vol. 25, no. 2, pp. 137–144.

3. Ershov E.D. Metody geokriologicheskih issledovanij. M.: Izd-vo MGU, 2004. 512 p.

4. Ershov E.D. Teplofizicheskie svojstva gornyh porod / E.D. Ershov, V. I. Artyushina, E. N. Barkovskaya i dr. Moskva: Izd-vo MGU, 1984. 204 p.

5. Komarov I.A. Termodinamika i teplomassoobmen v dispersnyh merzlyh porodah. M.: Nauchnyj mir, 2003. 608 p.

6. Motenko R. G. Opredelenie teplofizicheskih svojstv merzlyh, promerzayushchih i ottai-vayushchih neftezagryaznennyh zatorfovannyh gruntov s pomoshch’yu razlichnyh metodov / R. G. Motenko, D. V. Vlasenko, Yu. S. Kaloshina. Inzhenernaya geologiya, 2023, vol. XVIII, no. 4, pp. 64–78, https://doi.org/10.25296/1993-5056-2023-18-4-64-78.

7. Porhaev G.V. Teplovoe vzaimodejstvie zdanij i sooruzhenij s vechnomerzlymi gruntami. Moskva: Nauka, 1970. 208 p.

8. Hrustalev L.N. Osnovy geotekhniki v kriolitozone. M.: Izd-vo MGU, 2005. 542 p.

9. Cytovich N.A. Mekhanika merzlyh gruntov. M.: Vysshaya shkola, 1973. 448 p.

10. Chudnovskij A.F. Teplofizicheskie harakteristiki dispersnyh materialov. Moskva: Fizmatgiz, 1962. 456 p.