## 1 Introduction  
There are large areas of thick alluvium ranging from 400 to 600 m (or even over 700 m) distributed in parts of East, Central, North, and Northeast China, the lower part of which is rich in mineral resources. In order to develop the above resources, large-scale construction of deep shafts has been carried out in China since 2002. Therefore, China's coal resources have gradually entered into deep mining; for example, the thickness of the alluvium in the main shaft of Wanfu Coal Mine has reached 753.95 m. With the development of large-scale deep shaft construction, the safety of shaft lining structure design in deep shafts has encountered unprecedented challenges, and the study of deep soil mechanics has become a fundamental topic. The safety of the shaft lining structure in deep alluviums ultimately depends on the interaction between the shaft lining and geotechnical medium. This is the premise and key to carrying out shaft lining design and safety analysis in deep shafts to study the mechanical properties of deep soil under high stress [1]. In recent years, several shaft lining fractures have occurred in coal mine shafts built in deep alluviums in China [2; 3; 4; 5]. The main reason for the damage of most of the above-mentioned shafts is that the bottom gravel layer (hereafter referred to as the \"bottom aquifer\") of the thick alluvium that the damaged coal mine shaft passes through is mostly directly covered on the coal measure strata. Coal mine production leads to bottom aquifer hydrophobicity, which causes secondary consolidation and settlement of the soil around the shaft, resulting in additional vertical forces acting on outer edge of the shaft and ultimately causing shaft damage. The bottom aquifer of thick alluviums has obvious mechanical characteristics of high overlying total stress and a high water pressure (confined water). Furthermore, the problems of additional surface subsidence and shaft deviation caused by the bottom aquifer hydrophobicity of thick alluviums are also gradually becoming prominent [2; 6; 7], seriously threatening the production safety of mines and causing significant economic losses. Therefore, there is an urgent need for deep soil mechanics research to guide the prevention and control of related deep shaft hazards. The permeability of soil is one of the basic mechanical properties that characterizes the infiltration capacity of soil [8; 9]. The permeability coefficient (\(k_{v}\)) is a parameter that directly reflects the strength of soil permeability. The \(k_{v}\) of deep soil under high stress is an important parameter for calculating the hydrophobic settlement deformation of thick alluviums. More importantly, it forms the basis for revealing the evolution law of the vertical additional force of deep shafts under the effect of hydrophobic consolidation of the bottom aquifer of thick alluviums. At the same time, revealing the permeability law of the bottom aquifer is the basis for studying many coal mine engineering and geological safety issues [10]. For example, the use of bottom aquifer hydrophobicity depressurization to prevent water and sand surges in near-thick alluvium mining and grouting to control mine sand disasters. All of these situations require knowledge of the permeability characteristics of the aquifer in advance. Accordingly, many scholars at home and abroad have carried out a vast amount of research from different perspectives. In pore media permeability research, the variation of permeability with stress levels has always been of concern [11; 12]. Research on different samples shows that the confining pressure (\(\sigma_{r}\)) has an obvious influence on the \(k_{v}\) of the medium. [PERSON] [13] and [PERSON] [14] conducted triaxial permeability tests on saturated undisturbed loess and reshaped loess, with an \(\sigma_{r}\) ranging from 0.1 to 0.4 MPa, and found that their \(k_{v}\) decreased with increasing consolidation pressure, controlled dry density, and consolidation degree.