# Evolution Process of Toppling Deformations in Interbedded Anti-Inclined Rock Slopes
## 4 Discussion
### Uniqueness of the Interbedded Toppling
The width of the tensile fracture (\(\Delta d\)) can be obtained by:  
\[\Delta d=\frac{b}{sin\omega_{\text{d}}}-\frac{b}{sin\omega_{\text{t}}}, \tag{6}\]  
Figure 10: Deformation features of interbedded toppling events: **(a)** Typical deformation features of interbedded rock layers within a slope. Hard rock exhibits brittle fracture, while soft rock shows ductile bending deformation. The white dotted lines denote rock layers. The red dotted lines denote tensile fractures. The red arrows denote the direction of the tensile stress; **(b)** A typical toppling tends toward self-stabilization. The red dotted lines denote the toppling hinge surface. The white dotted lines denote rock layers. It should be noted that when \(\omega_{\rm t}>90^{\circ}\), the value of \(\Delta d\) begins to decrease. When \(\omega_{\rm t}\) and \(\omega_{\rm d}\) are complementary, \(\Delta d=0\). At this point, the side faces of rotated columns regain contact, and the rock layers exhibit a symmetrical structure about the THS (denoted as a mirror image condition). Rotation beyond the mirror image condition is impeded by the shear forces along rock layers, and the slope deformation tends towards self-stabilization (Figure 11c). The results of the base friction model test also indicate that the slope essentially satisfies \(\omega_{\rm d}+\omega_{\rm t}=180^{\circ}\) in a self-stable state (Figure 11d). Therefore, the mirror image condition of rock layers can serve as an indicator of the slope achieving self-stabilization. Despite the self-stabilization features of interbedded toppling bodies, there remains a risk of further catastrophic motion for toppled rock masses. This risk is associated with the extent of development of failure surfaces within the toppling bodies. Unlike the distinctive stepped failure surfaces formed by existing cross joints in block toppling (commonly considered as THS), the failure surface in interbedded slopes is related to the cross joints in hard rock columns and tensile fractures in soft rock columns. When cross joints connected tensile fractures among several rock layers, a localized toppling fracture zone can be formed (Figure 12a). Once several fracture zones intersect, a throughgoing failure surface can form, leading to the ultimate destabilization of the toppling bodies (Figure 12b). Note that the position of the failure surface in interbedded toppling bodies often lies above the THS [10; 11; 12]. This is because the intense weathering and unloading effects have shaped a more fragmented rock structure in the shallow zones of the slope. In addition, the accumulated overturning and bending steepen the tensile fractures near the slope surface, making the rock mass highly susceptible to sliding or overturning along these discontinuities and forming a longer tensile-shear fracture among several rock layers. Figure 11: Illustration of toppling at different periods: (**a**) Rock layers without deflection; (**b**) Rock layers with deflection; (**c**) Rock layers achieve self-stabilization; (**d**) Layer symmetry configuration in the physical model test.