Bending Strength of Frozen Soil Beam With Temperature Distribution and Consideration of Average Temperature Evaluation Method

Mathematical models of steady-state temperature fields produced by multi-piped freezing

“…(21) is consistent with the analytical solution derived by Tobe and Akimoto (1979) and Kato et al (2007), which is a particular solution of our solution when T 0 =0 °C. Another solution to the steady-state temperature field frozen by two freezing pipes with different temperatures was given by Hu and Zhang (2013a).…”

“…In this paper, soil is as assumed to be isotropic, and the temperature field of frozen soil is approximated to be steady state. These assumptions have previously been shown to be sufficiently accurate (Trupak, 1954;Bakholdin, 1963;Frederick and Sanger, 1968;Tobe and Akimoto, 1979;Kato et al, 2007). Heat exchange between the system and the environment is ignored because the calculation region is infinite.…”

“…Consequently, we can adopt steady-state rather than transient temperature fields to calculate the temperature field at a certain point in the freezing process. This viewpoint has been accepted in academic and engineering circles (Trupak, 1954;Bakholdin, 1963;Frederick and Sanger, 1968;Tobe and Akimoto, 1979;Kato et al, 2007).…”

“…Frederick and Sanger (1968) presented a simplified formula for a single-row-piped frozen temperature field. Tobe and Akimoto (1979) and Kato et al (2007) derived an analytical solution of a temperature field by multi-piped freezing with the pipes arranged in a straight line with equal spacing.…”

“…Analytical solutions of multi-piped frozen temperature fields, such as for two freezing pipe arrangements, plus three and four freezing pipes arranged in a straight line with equal spacing, were derived by Tobe and Akimoto (1979) and Kato et al (2007). However, there are no analytical solutions for three or four freezing pipes arranged in different forms.…”