Analytical solution to steady-state temperature field for row-type freezing tubes layout with non-zero freezing point

Artificial ground freezing (AGF) is widely used for ground stabilization and groundwater control in tunnel engineering, and accurate prediction of frozen-soil curtain thickness is essential for reliable design. Conventional analytical solutions generally assume a soil freezing point of 0 °C, which may lead to considerable errors in saline and offshore strata where freezing-point depression occurs. This study develops analytical solutions for the steady-state temperature fields of single-row and staggered double-row freezing-tube arrangements by combining velocity-potential theory with the hydrothermal similarity principle and incorporating a non-zero soil freezing temperature. The proposed solutions are validated against transient numerical simulations using parameters from a Shanghai Metro Line 2 connecting-channel project. The analytical and numerical predictions show good agreement: the relative difference is approximately 5%–15% during the early transient stage and decreases to less than 1% at approximately 30 days, as the transient temperature field approaches a quasi-steady state. In comparison, the conventional analytical solution based on a 0 °C freezing point exhibits larger discrepancies and overestimates the frozen-soil curtain thickness by approximately 10%–20% for the investigated saline-soil condition. The results demonstrate that incorporating the actual soil freezing point improves the reliability of analytical prediction and provides a practical analytical framework for estimating frozen-soil curtain thickness in saline and offshore underground engineering.