Precision of determination of thawing depth of the frozen rocks

Abstract

An important quantity determining the choice of technical solutions in design of both surface and underground structures in the permafrost area is the thawing depth of the rocks. To obtain simple analytical relations to determine the thawing depth over time, a simple assumption is used: that the initial temperature of the rocks is equal to the melting temperature of ice. The aim of the present work was the assessment of impact of this assumption on the forecast precision. For a quantitative assessment, a simple typical formula recommended by construction norms was used. Functional dependence of the density of the rocks and their heat capacity on the fraction of ice content was considered in the formulas. A rock consisting of a combination of quartz sand and ice was used as an example.Multiple variant calculations were done according to the formulas and their results presented in the form of charts. It was shown that the relative error in determination of thawing depth depends solely on the Stefan criterion and is independent of the thawing duration, thermal conductivity coefficient of the thawing rocks and the air temperature during the thawing. A relation was obtained which allows to quickly assess at which initial values (temperature and ice content of the frozen rocks) it is possible to use the formulas obtained from the simplified calculation models with the assumption that the temperature of the rocks is equal to the melting temperature of ice.