Evolution mechanism and deformation stability analysis of rock slope block toppling for early warnings

For massive engineering projects in high and steep mountain areas, toppling deformation, which is an important geological engineering problem in construction, has been observed. Three key issues in the early warning of toppling slopes are the boundary conditions, the evolution mechanism, and deformation stability analysis. This paper investigates an evolution mechanism for the timely prediction of block toppling-induced slope failure in rock masses and examines the relationship between boundary formation and the progressive development of toppling fracture planes. By describing an instantaneous toppling velocity field and identifying two possible fracture plane geometries (linear and parabolic), the optimal path of the toppling fracture plane is searched based on calculations of the critical toppling height (i.e., minimum load) and the upper bound theory of limit analysis. Regardless of the slope structures and mechanical parameters, the optimal path of the toppling fracture plane is straight and most likely oriented perpendicular to the bedding planes. Therefore, considering that structural damage will enable progressive toppling deformation instead of systemic failure, the evolution of block toppling deformation likely replaces the loop following the formation of the first fracture plane because the slope critical height is exceeded. In the loop, the deformation and inclination of columns is updated due to the formation and inclination of fracture planes, which may be perpendicular to the columns. This progressive formation of more inclined fracture planes leads to sliding collapse. The block toppling evolution is divided into 5 stages, and the instability criterion for the transformation of toppling deformation into sliding collapse is defined as the inclination of the fracture plane being equal to its friction angle. In addition, a PFC2D simulation of the entire slope toppling process is performed to verify this speculative evolution mechanism, and a satisfactory result is acquired. Finally, a deformation calculation model of slope block toppling is proposed for stability analysis in accordance with the instability criterion, which is further applied in a typical toppling case. The findings of this study provide a foundation for the deformation, stability and early-warning analysis of block toppling slopes.