## 2 Spatial Variability of Hydrothermal Parameter
### Anisotropic Spatial Variations  
The spatial variability of soft clay rock exhibits significant anisotropy, characterized by distinct directional variations in geotechnical properties. This anisotropy arises due to the orientation and arrangement of clay particles, which are influenced by factors such as sedimentation processes, depositional history, and mechanical loading conditions. In soft clay rock, the arrangement of clay particles tends to align along the principal stress directions, resulting in anisotropic behaviors in terms of strength, stiffness, and permeability. Moreover, the presence of soil structure and fabric further enhances the directional dependence of geotechnical properties. For instance, the orientation of clay platelets and micro-fabrics within the soil matrix can lead to pronounced variations in shear strength along different directions. Additionally, external factors such as loading history and environmental conditions can induce changes in the anisotropic behavior of soft clay rock over time. Understanding and characterizing the spatial variability and anisotropy of soft clay rock is essential for AGF applications [30; 31; 32]. In this study, the project background of this paper is that the section from Mengcheng Road Station to North Second Ring Road station of Hefei Rail Transit Line 5 is about 979 m long, the section roof is about 9.7-18.5 m, and the section floor is about 15.7-24.5 m buried. The shield method is intended to be used for construction; the tunnel diameter is about 6 m, and the formation constructed by the freezing method is soft clay rock. A series of soft clay rocks were collected, and thermodynamic tests were carried out. The range of DSC is 0\(\sim\pm\)500 mW, the temperature range is from \(-\)60 \({}^{\circ}\)C to 200 \({}^{\circ}\)C, the heating rate and cooling rates are 1\(\sim\)80 \({}^{\circ}\)C/min and 1-20 \({}^{\circ}\)C/min, respectively, the temperature resolution is 0.1 \({}^{\circ}\)C, the temperature fluctuation and repeatability are \(\pm\)0.1 \({}^{\circ}\)C, the noise is 0.01 uW, the resolution and accuracy are 0.01 uW and 0.1 uW. The sensitivity is 0.1 uW. Our DSC equipment comes from Germany. A known temperature difference is applied across a sample of clay, and the rate of heat transfer is measured. By calculating the heat flux and knowing the geometry of the sample, the thermal conductivity can be determined. Differentiating scanning calorimetry was used to measure the specific heat capacity. The sample is subjected to controlled temperature changes, and the heat flow into or out of the sample is measured. By analyzing the heat flow data, the specific heat capacity of the soft clay rock can be determined. The permeameter was used to assess the permeability. The constant head test is used in this paper. The inner diameter of the metal sealing cylinder, metal orifice plate, filter screen, pressure measuring pipe, and metal cylinder for the water supply bottle is 10 cm, and the height is 40 cm. The clay sample is placed in a permeameter cell, and water is allowed to flow through it under controlled conditions. By measuring the flow rate and applying [PERSON]'s law, the permeability of the clay can be calculated. The depth of the soil sample was 10 m, and 10 sets of samples were obtained. The test results of the hydrothermal parameters of soft clay rock for ten different sampling points are shown in Figure 1. It can be seen that the discrete features are very evident because of the heterogeneity of the soft clay rock. The relationship between spatial variation in anisotropy and heterogeneous characteristics of soft clay rock is significant. Soft clay rock exhibits anisotropic behavior due to variations in its mineral composition, fabric orientation, and depositional history. These variations lead to spatial heterogeneity in properties such as permeability, compressibility, and thermophysical properties. The alignment of clay particles along certain directions can result in preferential pathways for fluid flow, causing anisotropic permeability.