Determining representative length in analytical model for artificial ground freezing: A numerical study

Parameter ambiguity, particularly the representative length l denoting the overall scale of the frozen wall, frequently impedes the development of analytical models for artificial ground freezing. This study proposes a quantitative methodology for determining l using numerical simulations. After validating the coupled thermo-hydraulic solver against laboratory experiments, we conducted a parametric study of 12 pipe layouts under varying groundwater velocities. The results showed that the critical flow velocity decreased with the number of pipes owing to the hydraulic dam-up effect. Subsequently, a multiple linear regression model was used to predict l as a function of the total wall length, pipe density, and their interactions. This analysis revealed that a higher pipe density significantly improved the hydraulic robustness of longer frozen walls. The predictive model achieved a high coefficient of determination of 0.9771. By transforming l from a vague assumption into a predictable parameter for high-permeability soils, this study bridges numerical simulations and analytical models to enhance engineering design reliability. • A predictive model for the representative length ( l ) in AGF is proposed. • l is transformed from a vague assumption into a predictable design parameter. • A novel data analysis using hyperbolic fitting determines critical velocity. • Regression model predicts l from geometry with high accuracy ( R 2 = 0.977 ).