# Formation of a Freezing Wall Around a Vertical Shaft Under Localized Freezing
## 2 Technology of Shaft Lining Localized Freezing  
At present, freezing shafts in the deep soil layer are mainly double-layer composite shafts constructed with cast in situ reinforced concrete, and the shafts are mainly composed of the outer lining, the inner lining, and plastic plate interlayers between the inner and outer linings [25, 27]. The inner lining serves as a permanent water-sealing and load-bearing structure [30], while the outer lining primarily functions as a temporary support and is not required to seal water. Therefore, ensuring the safety of the inner lining is of utmost importance. For the double-layer composite shaft lining, the method of retrofitting the structure is usually used to manage shaft lining disasters [31]. Firstly, it is necessary to determine the location of the compressible devices based on geological data and place it as much as possible in the aquitard represented by the clay layer (Figure 2) [32]. Then, proceed with the three steps of \"slotting the inner shaft lining, installing the compressible devices, and repouring the concrete around the compressible devices\". Although the clay layer has a good waterproof effect, previous practical experience has shown that there are still risks of water inrush and sand collapse during the process of breaking the inner shaft lining and installing the compressible devices. In order to minimize risks during construction, it is necessary to use the freezing method to freeze and seal the cracks in the shaft linings and the strata near the slotting area.  
The shaft lining localized freezing method refers to the freezing process carried out by arranging layered and detachable circumferential freezing pipes at the inner periphery of the inner shaft lining, and the freezing area covers the proposed slotted area and a certain range above and below it. Vertical block detachable freezing pipes can also be selected according to the actual situation on site. Subsequently, thermal conductive adhesive is evenly laid between the freezing pipe and the shaft lining. Through low-temperaturefreezing pipes, highly thermally conductive adhesive, and insulation layers, the cold gradually transfers to the shaft lining and the outer strata, thereby blocking the water channel inside the concrete shaft lining and forming a freezing curtain in the target clay layer, as shown in Figure 2. As shown in Figure 3, during the structure retrofitting of shaft lining, the freezing pipes and other devices in the proposed slotting zone are removed, and the inner shaft lining is slotted and equipped with compressible devices. The rest of the freezing pipes remain in an active freezing state to prevent the melting of the freezing curtain.  
In this study, the thickness of the freezing wall behind the slotting zone reaching 1.2 m was used as the slotting criterion, and it was assumed that the shaft safety crisis can be completely resolved after installing the compressible device. Conservatively, the installation period of the compressible device is uniformly attributed to the shaft lining slotting period, during which it is assumed that the slotting position is completely exposed to the air. In summary, this study focuses on the formation and evolution of freezing walls in clay layers during the \"active freezing period\" and \"slotting period\" under the shaft lining  
Figure 3: Schematic diagram of layered detachable freezing pipes.  
Figure 2: Schematic diagram of the double-layer composite shaft structure and the process of adding a collapsible device with the assistance of localized freezing.