## 4 Simulation Verification
### Analysis of BBD Response Surface Method Results
When the unit-area normal stiffness is maintained at a constant level, the compressive strength increases in proportion to the rise in critical normal stress at low levels of unit-area normal stiffness. However, the growth trend is not sufficiently pronounced. In contrast, at high levels of unit-area normal stiffness, the compressive strength rises considerably with the increase in critical normal stress, exhibiting a growth trend that is more pronounced than that observed at low levels. When the critical normal stress is maintained at a constant level, the compressive strength exhibits a notable increase in correlation with the rise in normal stiffness per unit area. The response surface with a fixed unit area shear stiffness and critical normal stress is depicted in Figure 6c. When the critical shear stress is maintained at a constant level, the compressive strength demonstrates a notable increase in response to an increase in the normal stiffness per unit area. Furthermore, this growth trend is particularly pronounced. In contrast, when the typical stiffness per unit area remains consistent, irrespective of whether it is at a low or high level, the compressive strength exhibits minimal variation, and the trend is less discernible with the increase of the critical shear stress. In the context of a fixed unit area normal stiffness and critical shear stress, the response curves of unit area shear stiffness and critical normal stress are illustrated in Figure 6d. While the critical normal stress is maintained at a constant level, the compressive strength exhibits a slight increase with an increase in shear stiffness per unit area. This growth trend is relatively modest but nevertheless discernible. In contrast, when the shear stiffness per unit area is fixed, the low case demonstrates that the change in compressive strength is not readily apparent with an increase in critical normal stress. In the case of elevated critical normal stress, the compressive strength also increases, albeit at a relatively modest rate; this growth trend exceeds that of the shear stiffness per unit area. The response surface of unit area shear stiffness and critical shear stress with fixed unit area normal stiffness and critical normal stress is depicted in Figure 6e. When the critical shear stress is maintained at a constant level, it can be observed that in the case of low critical shear stress, the compressive strength increases significantly with the increase in the shear stiffness per unit area. This growth is evident and exhibits a clear trend. In contrast, in the case of high critical shear stress, the compressive strength decreases slightly with the increase of the shear stiffness per unit area, although the trend is less pronounced. At a constant unit area shear stiffness, the compressive strength exhibits a notable increase with the rise in critical shear stress in the low unit area shear stiffness case, demonstrating a discernible trend. Conversely, in the high unit area shear stiffness case, the compressive strength displays a slight decline with the increase in critical shear stress, and the trend is also relatively evident. The response surfaces of critical normal stress and critical shear stress are depicted in Figure 6f for a fixed normal stiffness per unit area and shear stiffness per unit area. When the critical shear stress is maintained at a constant level, an increase in critical normal stress results in an enhancement of compressive strength in the context of low critical shear stress. Conversely, in the case of high critical shear stress, an elevation in critical normal stress is accompanied by a reduction in compressive strength, thereby indicating a negative correlation. When the critical normal stress is maintained at a constant level, the compressive strength exhibits a contrasting behavior in response to the critical shear stress,depending on the level of the critical normal stress.