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Flexural toppling is typically observed in anti-dip bedding rock slopes with a set of steeply dipping parallel joints against the slope face. This failure occurs due to the bending of rock strata, similar to cantilever beams. However, the exact failure surface is usually unknown, which leads to an assumption regarding the location and shape of the failure surface that must be made in the theoretical analysis. This assumption serves as the basis for stability analysis but may lead to errors if it is not appropriate. Therefore, in this study, we provide a detailed and systematic review of the mechanical model, precondition, failure patterns of rock strata, primary controlling factors, morphological characteristics of slope failure surfaces, and theoretical analysis methods of slope stability. We also introduce two practical application cases to better understand the advantages, disadvantages, and application scope of these methods. Additionally, we discuss the existing issues and potential future research developments in this field. [ABSTRACT FROM AUTHOR]

As it is very difficult to construct conforming plate elements and the solutions achieved with conforming elements yield inferior accuracy to those achieved with nonconforming elements on many occasions, nonconforming elements, especially Adini's element (ACM element), are often recommended for practical usage. However, the convergence, good numerical accuracy, and high computing efficiency of ACM element with irregular physical boundaries cannot be achieved using either the finite element method (FEM) or the numerical manifold method (NMM). The mixed-order NMM with background cells for integration was developed to analyze the bending of nonconforming thin plates with irregular physical boundaries. Regular meshes were selected to improve the convergence performance; background cells were used to improve the integration accuracy without increasing the degrees of freedom, retaining the efficiency as well; the mixed-order local displacement function was taken to improve the interpolation accuracy. With the penalized formulation fitted to the NMM for Kirchhoff's thin plate bending, a new scheme was proposed to deal with irregular domain boundaries. Based on the present computational framework, comparisons with other studies were performed by taking several typical examples. The results indicated that the solutions achieved with the proposed NMM rapidly converged to the analytical solutions and their accuracy was vastly superior to that achieved with the FEM and the traditional NMM. [ABSTRACT FROM AUTHOR]