# Failure of Rock Slope with Heterogeneous Locked Patches: Insights from Numerical Modelling
## 3 Numerical Results  
### Strength Effect  
Figure 3a shows the failure process of the simulated rock slope with locked patches of the same uniaxial compressive strength. Shear stress concentrates obviously in the locked patches whereas the shear stress of the bedrock and the slide body are relatively low. As the shear stress grows, the left locked patch first begins to fail. The cracks initially occur at the top right corner and the bottom left corner of the locked patches. Then two parallel crack bands gradually expand along the interface between the locked patch and the bedrock and slide body symmetrically whereas little damage has been caused within the locked patch, bedrock, and slide body. The numerically reproduced stress localisation zone is consistent with the experimental results where the locked patch failed progressively with identifiable strain localisation zones [20]. The two locked patches exhibit similar failure modes and only when both locked patches are failed, the model becomes completely unstable. Therefore, the locked patch with higher shear strength and peak shear displacement controls the model stability. Namely, the shear strength and peak shear displacement of the model can be considered as the larger values of the two locked patches. The models with different strength locked patches have the similar failure pattern. Most cracks are distributed on the interfaces of locked patches while few cracks are found in the locked patch, bedrock, and slide body. Figure 3: _Cont._Figure 3b shows that the corresponding AE distribution is consistent with the shear stress distribution where the failure is mainly concentrated on the interfaces between the locked patch and bedrock and slide body. It shows that a large number of AE initially appears in the left locked patch, and then in the right locked patch, suggesting that the stress is being transferred from the left locked patch to the right one. For the slide body under shearing, the AE distribution demonstrates that the rockslide is mainly caused by tensile failure of the locked patch. In other words, the tensile failure of the elements leads to the macroscopic shear failure of the model. Figure 4 shows the shear stress-shear displacement-acoustic emission curves of the model with locked patches of different strength. In the early stage, shear stress-displacement curves of two locked patch basically overlap and little damage has been caused. The increasing displacement leads to the damage of locked patch and visible increase of AE counts and energy. AE can be divided into two parts, i.e., that released in the post-peak of the first broken locked patch and the failure of the second broken locked patch. AE distribution in Figure 3b indicates that little energy is released after the failure of the locked patch. Therefore, the second broken locked patch is responsible for the AE after the first peak stress. Figure 3: Failure of model with two locked patches of same strength: (**a**) shear stress distributions, (**b**) AE distributions. Figure 5 summarises the relationship between the strength of the locked patch versus peak shear displacement and shear strength. For convenience, the locked patch, shear strength, and peak shear displacement are abbreviated as LP, SS, and PSD, respectively, in the figure. It should be noted that the break of one locked patch does not cause the immediate failure of the rock slope. The maximum peak shear displacement of the last broken locked patch can be up to twice as much as that of the first broken locked patch  
Figure 4: Effect of strength on the relationships between shear displacement and shear stress, AE counts, and AE accumulative energy. (Figure 4). On the other hand, it shows that both the shear strength and peak shear displacement of the right locked patch increase as its strength becomes higher. The variation of the strength of the right locked patch poses little effect on the displacement of the left locked patch where the peak shear displacement of the left locked patch remains constant with small fluctuations.