# Flexural Buckling Failure of Rock Slopes: A Review of Influencing Factors and Analysis Methods
## 1 Introduction  
Under internal and external forces, layered rock masses in the upper portion of a dip slope may slide along weak structural planes, thus compressing the stratified rock masses in the lower portion and causing them to bend and bulge. When bending proceeds, the breaking of rock layers due to shearing or tension may occur at the slope toe, resulting successive failure [1, 2, 3, 4, 5]. The deformation and failure mechanism of flexural buckling is quite complex, involving the action of interlayer sliding in the active zone and bending uplift in the passive zone, as well as the dynamic adjustment of the boundary between the active and passive zones. Although such landslides usually experience a long period of time-dependent deformation before failure, they may cause significant casualties and economic damage if timely countermeasures are not adopted [6, 7, 8, 9, 10, 2]. For example, the Athytos highway landslide in the Central Macedonia region of Greece cut off the main road connecting the Chalkidiki peninsula with the mainland [6]. The Yokawatashi landslidein Niigata, Japan, resulted in three people missing and severe damage to several railway lines [11; 12]. The Shaiolin ancient landslide in southern Taiwan led to 397 fatalities and hundreds of millions in economic losses [4]. The largest Dhampu-Chhoya landslide occurred along a 20 km stretch of the Kali Gandaki River (one of the largest rivers traversing southward from Tibet to India through the High Himalayas), temporarily damming the river and causing dramatic morphological changes [13]. With an estimated debris volume of 4.9 \(\times\) 10\({}^{7}\) m\({}^{3}\), the Xiaguiwa landslide impacted the Jinsha River, SE Tibetan Plateau, forming a dam over 60 m high that temporarily blocked the river [14; 15; 16]. Thus, the research on the deformation and failure mechanism of buckling landslides under the coupled action of internal and external forces, as well as the corresponding methods for stability evaluation and run-out analysis, holds significant scientific and practical value. This is particularly true for the identification, monitoring, early warning, and risk prevention and control of such landslides.  
However, the refinement and advancement of theoretical knowledge on the flexural buckling failure of dip rock slopes are often constrained by existing analysis methods. For flexural buckling failure, since the potential sliding surface does not daylight on the slope face but dips into the slope toe, the formation of a rupture surface involves complex geological and mechanical processes. Assessing the stability condition and changing trend of such a landslide is intricate and challenging. Consequently, existing quantitative methods for the stability analysis of buckling landslides need to simplify this aforementioned complex process equivalently, which leads to the applicability and consistency of a variety of approaches that usually cannot achieve satisfactory results and are worth further discussion.  
For this purpose, this study comprehensively reviews the current research achievements related to buckling landslides, following the research path of \"triggering mechanism \(\rightarrow\) analysis methods\". This study re-examines the intrinsic and triggering factors influencing the deformation process of flexural buckling failure, as well as the existing physical, analytical, and numerical methods. Finally, this study summarizes the primary deficiencies in the research field of buckling failure and outlines the future research directions.