Generalized analytical solution to steady-state temperature field of single-row-piped freezing

Artificial ground freezing method (AGF), which turns the water in the soil into ice, improves soil’s bearing capacity itself.It is an ideal reinforcement and waterproof for the under-ground engineering.In the soft soil area with high underground water table, AGF is widely used in the project for tunneling machine launch or retrieval and the row pipes and the ring pipes are the common forms.The mechanical properties of the frozen soil are inseparable from the pipe form and temperature distribution, so it is important for the researchers in the freezing project to understand the temperature field distribution of different piping forms.The most popular method is to treat freezing as a quasi-steady state process and approximate the temperature field distribution using a steady-state formula.In terms of all analytical solutions of single-row-piped freezing, it is only available for the steady-state temperature field of the simple form.However, there is no solution for the generalized single-row-piped freezing.Based on the periodic model of Бахолдин arrangement and Dirac function, this paper establishes a periodic steady-state model and obtains its analytical solution by Green’s function method.Then, the steady-state temperature field of the generalized single-row-piped arrangement, as a matrix form, is derived.Finally, a special pipe form is simulated to test the accuracy and applicability of the analytical solution.The results show that since the frozen soil has not been intersected and the heat exchange is severe in the early stage, there is a certain error between the analytical solution and the numerical calculation.Nevertheless, the overall change trend is consistent.When the frozen soils develop for a period of time, the heat exchange tends to be stable and the analytical solution is very consistent with the numerical calculation, which means the analytical solution can be used to estimate the transient temperature field distribution.