###### Abstract  
Artificial ground freezing (AGF) technology has been commonly applied in tunnel construction. Its primary goal is to create a frozen wall around the tunnel profile as a hydraulic barrier and temporary support, but it is inevitably affected by two natural factors. Firstly, seepage flows provide large and continuous heat energy to prevent the soil from freezing. Secondly, as a key soil parameter in heat transfer, the soil thermal conductivity shows inherent spatial variability, binging uncertainties in freezing effects and efficiency. However, few studies have explored the influence of spatially varied soil thermal conductivity on AGF. In this study, a coupled hydro-thermal numerical model was developed to examine the effects of seepage on the formation of frozen wall. The soil thermal conductivity is simulated as a lognormal random field and analyzed by groups of Monte-Carlo simulations. The results confirmed the adverse effect of groundwater flow on the formation of frozen wall, including the uneven development of frozen body towards the downstream side and the higher risk of water leakage on the upstream face of the tunnel. Based on random finite element analysis, this study quantitively tabulated the required additional freezing time above the deterministic scenario. Two levels of the additional freezing time are provided, namely the average level and conservative level, which aim to facilitate practitioners in making a rule-of-thumb estimation in the design of comparable situations. The findings can offer practitioners a rule of thumb for estimating the additional freezing times needed in artificial ground freezing, accounting for the seepage flow and spatial variation in soil thermal conductivity. artificial ground freezing; frozen wall; seepage flow; thermal conductivity; random field +
Footnote †: journal: Applied Sciences  
**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. **Published:**effects and an additional freezing time was required to be longer with the increase of an inaccuracy level. [PERSON] et al. [11] designed a controlled laboratory scale experimental rig to mimic the AGF process and the results indicated that the flow rate of the refrigerant had a high effect on the closure time of frozen wall. [PERSON] et al. [12] reported that the spacing between freeze pipes could significantly impact the freezing time and shape of the frozen body. These factors are expected to be more carefully considered or even solved with corresponding measures and with a greater maturity of technology. However, two natural and inevitable factors, namely, groundwater seepage and uncertain soil thermal properties, are likely to affect the freezing evolution and final freezing effects of the AGF technique. Firstly, groundwater flow with a high velocity can provide steady and continuous heat to delay or even prevent the closure of a frozen wall. [PERSON] and [PERSON] [13] investigated the impact of groundwater flow on the formation of a frozen wall and found that the connection between adjacent frozen piles would be delayed when the seepage flow is high. [PERSON] et al. [14] carried out three-dimensional ground freezing simulations under high seepage flow velocity conditions, and the progression of the freezing front was found to be asymmetrical, which extended more in the flow direction. Both [PERSON] et al. [15] and [PERSON] et al. [16] suggested that seepage would affect the position and the shape of the formed frozen wall and two different optimization methods were presented to get a better arrangement of the freeze pipes. Secondly, the mechanical properties of the frozen soil show a strong dependence of temperature and its strength increases with the decrease in temperature [7; 8]. Therefore, the thermal properties of soil should be paid more attention to in the theoretical research and construction design of the AGF technique. In this regard, [PERSON] et al.