# Flexural Buckling Failure of Rock Slopes: A Review of Influencing Factors and Analysis Methods
## 3 Deformation Process of Flexural Buckling Failure and Its Influencing Factors
### Factors Affecting the Deformation Process of Flexural Buckling
#### 3.2.1 Intrinsic Factors
In engineering practices, reinforcements such as anchor rods, anchor cables, and anti-sliding piles can be selected according to specific situations, as well as preventions of water-induced softening of basal sliding surface. (3) Dip angle of rock layer  
In general, the slope stability against flexural buckling gradually decreases with the increase of the dip angle of rock layer [23; 29; 36; 40; 48; 49]. The main reason is that an increased dip angle leads to high bending moments and shear forces in the stratified rock mass, and the self-weight component parallel to basal sliding surface also increases, intensifying the risk of flexural buckling failure. For dip rock slopes consisting of medium-soft rocks, such as marl, slate, phyllite, shale, [PERSON] et al. [29] conducted a systematic and in-depth study on the influence of dip angle combing model testing and numerical simulation. By monitoring the deformation of slope model, it was found that when the dip angle of the rock layer was 20\({}^{\circ}\), the slope model only underwent slight deformation; with the increase of the dip angle, the rock layers exhibited creeping deformation, and the rock layers of the lower part of the slope model showed bending phenomena; when the dip angle of the rock layer was less than or equal to 20\({}^{\circ}\), the front edge of the slope model was usually relatively stable and did not uplift. Based on the above phenomena, [PERSON] et al. [29] believed that a dip angle of rock layer greater than 20\({}^{\circ}\) is an important geological condition for the buckling instability of dip slopes with medium-soft rocks. Recently, [PERSON] et al. [50] statistically investigated the relationship between the instability deformation of buckling landslides and the dip angle of the strata, pointing out that the dip angles of rock layers with buckling deformation are mostly distributed between 20\({}^{\circ}\) and 50\({}^{\circ}\). The main reason is that rock layers with a gentler dip angle generally undergo bedding sliding-tension cracking, while rock layers with a steeper dip angle are mostly dominated by toppling deformation. It should be noted that buckling failure can also occur in very steep rock layers when the boundary condition of the layer toe is pinned, owing to the fracturing and loosening [1]. Table 1 also lists the dip angle information of nine typical buckling landslides. As can be seen from the table, the dip angles of the above buckling landslide cases generally  
Figure 4: Relationship between shear strength parameters of basal sliding surface and critical slope length (data from [PERSON] et al. [48]). vary between 20\({}^{\circ}\) and 50\({}^{\circ}\), fully corroborating the research conclusions of [PERSON] et al. [50]. Therefore, extra caution should be exercised when encountering this dip angle range in the site. (4) Deformation parameters of rock mass  
At present, there is relatively little research on how deformation parameters of rock mass influence the buckling stability of rock slopes. In this respect, most studies use theoretical analysis to explore these relationships [36; 41; 49; 51]. The relationship between critical length and the deformation modulus is often nonlinear positive, as shown in Figure 5. The reason is that intact rock with high elastic moduli has strong sectional bending performance and is not prone to plastic deformation, thus exhibiting better buckling stability. From the perspective of lithology, the elastic modulus of intact rock can indirectly reflect the strength of the rock. Soft rocks with lower elastic moduli are more prone to buckling failure due to their poor bending and shear resistance. For instance, in the field investigation of the deformation and failure modes of rock slopes in soft rocks, [PERSON] [21] found that buckling dominates when the boundary conditions of the rock layer are fixed.