The Temperature Field in Shaft Freezing

Abstract

The equations of heat conduction are numerically solved for two kinds of artificial freezing-traditional freezing and liquid nitrogen freezing. Both methods of ground freezing have been used in China for unstable, water-bearing strata.
In this paper a two-dimensional finite difference model simulating the freezing field is developed. The procedure introduces a way to simulate the effect of latent heat released when water undergoes a phase transformation from liquid to solid, and a way to calculate the harmonic mean of heat conductivity used when dealing with heterogeneous material.
The theoretically derived temperature distributions in frozen soil are given in detail and compared with measured data. Realizing that the equation of heat conduction is difficult to solve analytically and that the laborious task of temperature measurements in situ, the numerical method and the computer simulation presented here are expected to be useful for continued research in frozen soil and shaft freezing technology.