# Formation of a Freezing Wall Around a Vertical Shaft Under Localized Freezing
###### Abstract
As the distance between the freezing pipes increases, the time for the freezing walls to intersect increases linearly; the temperature of the freezing walls decreases with the decrease in the distance between the freezing pipes, and the strength of the freezing walls becomes more uniform. Despite decades of significant advancements in AGF technology, the freezing method employed for shaft lining retrofitting has seen little innovation, and the conventional approach of drilling freeze pipes around the shaft to establish frozen walls remains the standard practice. Due to the principal limitation of the freezing method by circulating freezing fluid through buried freezing pipes around the vertical shaft, it is difficult for the freezing wall to fully adhere to the shaft lining under external freezing conditions [22]. Therefore, the external freezing method typically employs full-depth freezing to eliminate the risk of  
Figure 1: Onsite photo of shaft lining disaster: (**a**) concrete spalling and inward bending of longitudinal steel bars; (**b**) spray water and sand at ruptured shaft lining in soil layer section [1]. water-conducting channels persistently existing between the shaft lining and the freezing wall [23]. However, the external full-depth freezing method has numerous drawbacks. Firstly, it is expensive. To protect the shaft lining, the distance between the freezing holes and the shaft must be increased, leading to an enlargement of the freezing circle's diameter and a surge in the number of freezing holes/pipes [24, 25]. Coupled with full-depth freezing, the construction cost of the external freezing method is extremely high. Taking the shaft lining failure remediation project at the main shaft of Chensilou Coal Mine in China as an example, the freezing cost alone exceeded RMB 36 million [22]. Secondly, the construction process is cumbersome. Before active freezing, steps such as \"hole selection, drilling, pipe insertion, and pipe fixation\" need to be carried out for external full-depth freezing [26, 27]. Additionally, selecting the locations for external freezing holes is challenging. The cracked shafts in deep overburden are often old or existing shafts with complete surrounding facilities, leading to conflicts between the designed positions of the freezing holes and existing structures [28]. To address this issue, buildings may have to be demolished, freezing holes might need to be expanded, the number of freezing holes could have to be increased, or even \"S\"-shaped directional holes may need to be drilled [29], further causing a sharp rise in project costs. In response to the cumbersome construction process and high costs associated with the external full-depth freezing method for creating a freezing curtain during vertical shaft repair, this paper innovatively proposes a localized freezing technique on the inner periphery of vertical shafts, and the influence of freezing temperature, lining thickness, slot height, and slot duration on the evolution of freezing walls in clay layers is analyzed based on a hydro-thermal coupled numerical model in COMSOL 6.0. The research findings hold significant scientific and engineering importance for the innovation of manufacturing methods for artificial freezing curtains around deep vertical shafts.