A novel determination method for thermal boundary conditions during permafrost simulation

Abstract

Boundary conditions are crucial for simulating the thermal status of permafrost soils, impacting the assessment of infrastructure stability and permafrost degradation. Field measurement and the boundary layer theory are two principal methods to determine the thermal boundary conditions, while parameters in these methods are empirical. This study proposed a novel method to determine the thermal boundary conditions, utilizing the known active layer thickness (ALT) and the depth of permafrost base. Firstly, the accuracy of equations for estimating ALT and the depth of permafrost base was validated using observed data. Next, a numerical model was built to investigate the impact of changes in ALT and the depth of permafrost on its thermal state. And then, the major influencing parameters of ALT and the depth of permafrost were determined. The results indicated that: (1) The maximum relative error between the observed and the estimated ALT is 15 %, and ALT can be reasonably estimated by the extended Stefan equation for multi-layered soils; (2) The maximum relative error between the observed and the estimated depth of permafrost is 4.9 %, and the depth of permafrost base can be estimated by the newly modified equation; (3) As two crucial indicators to judge the reliability of thermal boundary conditions, ALT and the depth of permafrost base needs to be appropriately set to avoid unacceptable deviations in numerical simulation. In this study, the relative error between the numerically inversed and the observed temperature was only 5.4 %, with an appropriate ALT of 2.5 m and a depth of 44.52 m for the permafrost base; (4) ALT is mainly governed by surface thawing index and water content, while the depth of permafrost base is mainly governed by geothermal gradient and mean annual ground temperature (MAGT). Based on the results, a method for determining the upper temperature and the lower heat flux boundary is proposed for permafrost simulation. The findings can guide the design and numerical simulation of geotechnical engineering in permafrost regions.