# 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  
(1) Thickness of rock layer  
From the perspective of material mechanics, the thin-layer rock mass with lower cross-sectional bending stiffness is prone to buckling instability. [PERSON] et al. [29] believed that the influence of rock layer thickness on the buckling stability is mainly reflected in the buckling depth (buckling depth equals the number of bending rock layers multiplied by the single-layer thickness of rock); the thicker the single rock layer, the more pronounced its decisive role in the overall bending stiffness and the final buckling state. Through the experimental investigation of the deformation and failure features in catacinal slopes, [PERSON] and [PERSON] [30] indicated a negative relationship between the buckling stability and the single-layer thickness. Later, the aforementioned negative relationship, in other words, the positive relationship between the critical slope length/height and the single-layer thickness, has also been demonstrated through sensitivity analyses using various analytical approaches [36; 40; 41]. Table 1 presents data on the geometry (including layer thickness) of typical events of flexural buckling failure [3; 14; 42; 43; 44; 45; 46; 47]. According to the Chinese Code for Investigation of Geotechnical Engineering (GB50021-2001, 2009), the thickness of a single rock layer can be classified into four categories: very thick (>1.0 m), thick (0.5 m \(\sim\) 1.0 m), medium-thick (0.1 m \(\sim\) 0.5 m), and thin (<0.1 m). The data indicate that the majority of flexural buckling failures occurred in the thin and medium-thick rock layers, with occurrences also noted in  
Figure 3: Deformation process of flexural buckling failure: (**a**) slight bending stage; (**b**) intense bending and uplift stage; (**c**) shearing failure and landslide stage. very thick rock layers. The reason for that feature is that the ratio of singe-layer thickness to slope length or height remains relatively small, leading to buckling deformation of the rock layer with high flexibility. (2) Strength parameters of basal sliding surface  
Based on the deformation process of flexural buckling failure, the shear strength parameters of basal sliding surface (cohesion and internal friction angle) directly affect the residual sliding force of rock masses in the active zone, which finally induces the bending of layered rock masses in the passive zone, altering the buckling stability of rock slope accordingly. At present, the effect of shear strength parameters of basal sliding surface on the flexural buckling stability is mainly investigated using analytical approaches. Referring to the [PERSON] et al. (2018) and [PERSON] et al. (2014), the relationship curves between the buckling stability indicators and the shear strength parameters of basal sliding surface generally follow the same pattern of change, as shown in Figure 4. From the figure, it can be seen that as the cohesion or internal friction angle of basal sliding surface increases, the critical slope length for buckling failure first shows a linear and gentle growth trend in the bending-dominated stage. However, when the cohesion or internal friction angle of basal sliding surface exceeds a certain critical value, the critical slope length for buckling failure increases sharply and abruptly during the sliding-dominated stage. The reason lies in the fact that when the shear strength parameters of basal sliding surface increase to a certain extent, the anti-sliding force acting on the upper-middle part of the slope is greater than the sliding force, then the interlayer sliding in the upper-middle part of the slope will cease and the compression effect exerting on the layered rock mass of the lower portion will disappear, hence the critical slope length for buckling instability increases sharply. According to above analyses, it is theoretically feasible to increase the slope stability against flexural buckling by enhancing the shear strength of basal sliding surface.