Artificial ground freezing: A review of analytical solution to steady-state temperature field

Benefit from water sealing advantages, artificial ground freezing method is widely applied in the construction of underground engineering. Compared with conventional ground improvement technique, it has the advantage of green, low-carbon and pollution-free. Temperature serves as a key indicator for assessing whether the frozen soil curtain has achieved the required thickness. The analytical solution of the steady-state temperature field is an effective method for predicting the temperature development state of frozen soil curtain. A comprehensive overview of related publications that discuss analytical solutions to steady-state temperature field of the frozen soil curtain under various tube layouts is provided in this paper. These layouts can be categorized into various types, such as a single tube, a few tubes, row-type tube layouts (single row, double rows, triple rows and multiple rows), circle-type tube layouts (single circle, double circles and triple circles), and other condition of asymmetric temperature distribution due to the seepage. Several numerical solutions, such as boundary separation method, potential function superposition method, and conformal transformation method are utilized to derive the analytical solutions. This review offers a relatively all-sided summary of the current analytical solutions to the steady-state temperature field, thereby contributing to the advancement of temperature field theory of artificial ground freezing.