## 4 Results and Discussion
### Porosity along the Vertical Direction  
Porosity is an important fundamental parameter in the evolution process of broken rock masses [48]. Different from previous studies on the porosity of broken rock mass [26; 39; 40], this paper innovatively uses the slice method to visually display the porosity change along broken rock mass in the Z-axis space, which can more accurately study the spatial distribution characteristics of porosity along the seepage direction and provide a better theoretical basis for the evaluation of the permeability characteristics of thermal storage mine water. The model was divided into 1000 slices along the z-axis at different  
Figure 11: Fracture pattern diagram of broken rock mass.  
strain levels of 0.075, 0.175, 0.275, and 0.375, and the corresponding porosity of each slice with different size grading distributions in the broken rock mass was recorded, as shown in Figure 12.  
Figure 12: Space distribution of porosity in broken rock mass during the lateral confinement compression process and water immersion. (**a**) Porosity of broken rock mass with size grading G1; (**b**) Porosity of broken rock mass with size grading G2; (**c**) Porosity of broken rock mass with size grading G3; (**d**) Porosity of broken rock mass with size grading G4; (**e**) Porosity of broken rock mass with size grading G5.  
As shown in Figure 12, the initial broken rock mass sample undergoes symmetrical compressive deformation along the z-axis due to the influence of axial stress. The porosity at the starting and ending parts of the z-axis is zero, whereas non-zero porosity indicates the presence of a broken rock skeleton structure at that location. The porosity of broken rock mass decreases with increasing strain, and the porosity curve along the z-axis fluctuates and decreases as strain increases, indicating a more uniform distribution of rock blocks. When the strain reaches 0.275 and 0.375, significant symmetrical fluctuations in the broken rock mass porosity curve are observed at both ends of the z-axis. This is believed to be caused by the increased displacement of particles at both ends of the broken rock mass when the strain becomes too high. It results in a certain difference in displacement between adjacent particles above and below, leading to collisions between them and causing fluctuations in porosity.  
The porosity of broken rock mass is related to its permeability characteristics, which directly affect the efficiency of extracting water with heat from the abandoned mine. To analyze and study the influence of particle size grading distribution on the porosity of broken rock mass, the variation law of average porosity with strain for broken rock mass with different size grading distributions is shown in Figure 13.  
According to Figure 13, the overall porosity of broken rock mass under lateral compression decreases gradually with strain, and the curve trend is similar for different size grading conditions. The difference in mean porosity between G1 and G3 is small, with a maximum value of 0.045, and the value increases first and then decreases. According to the study on the grading of rock mass in goat formation under different lithological roof strata [14], the size grading of the broken rock mass in the goat tends to be closer to G1, G2, and G4. When the particle size proportion decreases monotonically with particle size (G4), the porosity of the broken rock mass samples is consistently highest. At this time, the efficiency of extracting thermal mine water from abandoned mines can be relatively improved.