## 4 Results Analysis
### Stress Evolution and Failure Mechanism  
The visualisation of the stress field is an invaluable technique for observing the failure process and analysing crack behaviour [57]. Principal stress axes serve as an effective tool for depicting the state of stress and the orientation of the principal stress directions, which can greatly aid in the analysis of failure mechanisms [58; 59]. To capture the stress field within the sample, a total of 1727 measurement circles were arranged, as depicted in Figure 10. These measurement circles were designed with an overlap to ensure the acquisition of more detailed and comprehensive stress data. The horizontal, vertical, and shear stress values monitored by these measurement circles were extracted and utilised to calculate the maximum and minimum principal stresses. Furthermore, the \"Tensor\" tool within the PFC software was employed to plot the principal stress axes, which were drawn by importing the stress values. As presented in Figure 11, the long line at the stress cross in the figure signifies the direction of the maximum principal stress, while the short line indicates the direction of the minimum principal stress. Compressive stress is shown as positive and tensile stress as negative in the colour representation of the stress values. For an in-depth examination, five different states of sample \"S-2\" were chosen in order to obtain better knowledge of the failure process. Point B (Figure 11a): The maximum value of the maximum principal stress is observed at the left root of the first step. In this step, the minimum principal stress is nearly zero, and the direction of the maximum principal stress deflects counterclockwise by approximately 60 degrees (noting that the maximum principal stress direction is vertical during the servo stage). The first step is in a point-load stress state, which could lead to splitting failure. Because of its biaxial compression, the rock slab is the primary vertical load-bearing element. Point C (Figure 11b): Following the attainment of bearing capacity limitations, splitting cracks appear in the first step (refer to Figure 7). The propagation path of these cracks aligns with the direction of the maximum principal stress identified at Point B. A pronounced concentration of the maximum principal stress is evident on both sides of the first step root and the left root of the second step. The horizontal direction in rock slab 2, the leftward deflection direction in rock slab 3, and the counterclockwise deflection in the second rock step make up a whole maximum primary stress transmission path. Point D (Figure 11c): The direction of the maximum principal stress in the first rock step gradually deflects towards the vertical direction. This indicates that the first rock step has lost its bearing capacity, which is also evident from the significant stress concentration at the left root of the second rock step. The two sides of rock slab 2 continue to bear the majority of the minimal principal stress. At the interface of rock slab 3 and the second rock step, there is slight tensile stress. Figure 10: Arrangement of measurement circles. Figure 11: Cont. Point F (Figure 11d): As the shear displacement increases, the particles in the first rock step are compressed. The stress concentration in the first rock step reemerges due to particle re-contact. The left root of the third rock step becomes the primary location of the stress concentration. The fracturing of the lower rock slabs results in the disrupted continuity of the stress distribution. Point H (Figure 11e): After all rock steps have failed, the maximum principal stress in the first rock step deflects to a near-vertical direction, making it the main location to bear normal stress at the residual stage. The direction of the maximum principal stress in the second rock step and rock slab 3 is near horizontal, with the minimum principal stress being almost zero, indicating that this area is the origin of residual shear stress.