# Optimization Design Study of Pipe Curtain Freezing Scheme for Sanya Estuary Submarine Channel
## 1 Introduction  
The rapid urban economic development is characterized by a significant influx of people to economically thriving cities, leading to increased population pressure and insufficient above-ground space. Consequently, many countries are turning to the full development and utilization of underground space as a preferred solution to this issue [1; 2]. However, the development of underground space faces numerous complex engineering challenges. Particularly in eastern China, where the hydrological system is complex, underground engineering must also account for the effects of groundwater on construction. Conventional construction techniques are not suitable for areas rich in water and with weak strata. To address this, people have developed and proposed a method known as artificial freezing technology, which involves freezing the natural environment. This technique also referred to as the artificial freezing method, has been widely applied in water-rich and weak strata regions [3; 4; 5; 6]. However, when the volume of construction permafrost is too large, the soil expands excessively upon freezing and produces settlement displacements when itmelts [7; 8; 9; 10]. In order to reduce the impact of frost heave and thaw settlement on construction, scholars have combined the pipe curtain method with freezing methods to create the pipe curtain freezing method [11]. The pipe curtain freezing method represents a significant advancement in artificial ground freezing technology, integrating the principles of pipe curtain technology with artificial ground freezing. In this method, the pipe curtain support structure serves as the primary load-bearing system, while the frozen soil curtain, generated through the application of artificial ground freezing technology, primarily functions as a water barrier [12; 13; 14; 15]. The Gongbei Tunnel, a component of the Hong Kong-Zhuhai-Macao Bridge Zhuhai Link Road project, is situated in a section characterized by saturated soil, high compressibility, and high permeability. To ensure the safety of construction personnel while preserving the integrity of existing ground structures and underground utilities, the construction team adopted the pipe curtain freezing method, a technique that has been successfully applied for the first time in domestic tunnel engineering [16; 17; 18; 19; 20]. In recent years, many scholars have made some achievements in the research of the pipe curtain freezing method. [PERSON] et al. conducted a numerical analysis of the freezing project for the new west ventilation shaft at Yandian No.2 Mine in Huaibei Coalfield, employing a water-heat coupling model for the freezing temperature field based on the theory of mixed media. The analysis compared field measurement data with numerical calculation results, revealing that a greater proportion of water in the soil body inside the freezing pipe circle froze into ice compared to that outside the circle. This indicates a more pronounced phase change in the soil body within the freezing pipe circle [21]. [PERSON] et al. conducted a study to investigate the evolution of the three-dimensional non-uniform freezing temperature field. To achieve this, they established a tunnel level freezing model test system based on the similarity criterion of hydrothermal coupling. The system was equipped with thermocouple temperature sensors to measure temperatures in three sections. The findings indicate that there are three cycles of temperature decrease curves at the measurement points: a sharp decrease, a slow decrease, and stabilization. The temperature profiles on both the primary and secondary planes of the frozen wall exhibited a V\" shape [22]. [PERSON] et al. investigated the distribution law of freezing and expansion within the seepage layer during tunnel construction using the horizontal freezing method. Their findings indicated that the rate of expansion for the upstream frozen wall was notably slower than that of the downstream wall, and the freezing temperature field was symmetrical along the seepage direction.