Average temperature calculation for straight single-row-piped frozen soil wall

The average temperature of frozen soil wall is an essential parameter in the process of design, construction, and safety management of artificial ground freezing engineering. It is the basis of calculating frozen soil's mechanical parameters, further prediction of bearing capacity and, ultimately, safety evaluation of the frozen soil wall. Regarding the average temperature of single-row-piped frozen soil wall, this paper summarizes several current calculation methods and their shortcomings. Furthermore, on the basis of Bakholdin's analytical solution for the temperature field under straight single-row-piped freezing, two new calculation models, namely, the equivalent trapezoid model and the equivalent triangle model, are proposed. These two approaches are used to calculate the average temperature of a certain cross section which indicates the condition of the whole frozen soil wall. Considering the possible parameter range according to the freezing pipe layout that might be applied in actual construction, this paper compares the average temperatures of frozen soil walls obtained by the equivalent trapezoid method and the equivalent triangle method with that obtained by numerical integration of Bakholdin's analytical solution. The results show that the discrepancies are extremely small and these two new approaches are better than currently prevailing methods. However, the equivalent triangle method boasts higher accuracy and a simpler formula compared with the equivalent trapezoid method.