# Optimization Design Study of Pipe Curtain Freezing Scheme for Sanya Estuary Submarine Channel
## 1 Introduction
The vertical freezing expansion displacement on the surface was observed to decrease as the tunnel depth increased, with the location of the maximum value remaining consistent with the increase in tunnel depth [23]. [PERSON] and colleagues focused on the challenge of analyzing the temperature field during well drilling using the artificial freezing method in the Cretaceous formation. They conducted numerical simulations and experimental measurements of the temperature field, establishing a numerical model for the freezing project's temperature field. This model predicted and analyzed the effective thickness of the freezing wall, the average temperature, and the wellbore wall temperature at various depths. A comparison of the measured temperatures from a test hole with those of the well wall indicated that the numerical simulation results closely matched the experimental data. [PERSON] et al. have highlighted the issue of insufficient temperature monitoring data and the complexity of numerical models, which impede the accurate prediction of complete frozen curtains in engineering applications. They proposed a coupled thermal and humidity model to predict the dynamic formation of frozen curtains. The findings indicate that hydraulic parameters can be derived from NMR measurements. The numerical model was also validated through indoor tests under various seepage conditions [25]. [PERSON] and colleagues investigated the phenomenon of artificial freezing in clay-sand strata under conditions of seepage, which involves coupled processes of water-ice-salt crystallization and heat-force transfer. Their findings indicated that the profiles of ice content, crystallized salt content, and adsorbed salt content within the clay-sand formation exhibited a non-linear distribution with a pronounced curve at the interface. The higher crystallized salt content in the clay layer compared to the sand layer was attributed to the effects of water seepage and heat conduction. The distribution profile of soil deformation in the clay-sand layer was observed to be bilinear [26]. As evidenced by the existing literature, experts and scholars have conducted research on the reinforcement mechanism of the pipe curtain freezing method and the changing laws of the freezing and thawing temperature field through actual measurements, indoor experiments, and numerical simulations. Despite this, relatively few domestic projects have adopted the pipe curtain freezing method in underwater tunnel excavation, making it necessary to explore its application in this context. This paper presents a case study of the pipe curtain freezing method used in the Sanya Estuary Undersea Tunnel project, employing COMSOL finite element software (version 6.0) to establish a three-dimensional water-heat coupling model for the numerical simulation of the temperature field. The research focuses on the development and distribution laws of the permafrost curtain and temperature field of this project. The dynamic simulation of the permafrost curtain evolution is primarily concerned with its development, circular intersections, average temperature, and effective thickness changes. Based on the simulation results of the original scheme, the paper conducts an optimization design of the freezing scheme and compares the changes in the permafrost curtain thickness under the optimized scheme. The findings of this project can serve as a theoretical reference for the design of similar projects in the future.