The Evolution Mechanism of the Slope Toppling Deformation for Early-Warning Analysis

With massive engineering projects performed in high and steep mountain areas, the evidence of toppling deformation, which has been an important engineering geological problem in construction, has been exposed and observed in quantities. Three key issues in the early warning of toppling slopes are the boundary condition, evolution mechanism, and deformation stability analysis. This paper investigates an evolution mechanism for timely predicting the occurrence of toppling induced slope failure in rock masses, relates boundary formation and progressive development about toppling fracture planes. By describing an instantaneous toppling velocity field and identifying two possible fracture plane geometries (linear and parabolic), the optimal path of toppling fracture plane is searched via critical toppling heights (i.e., minimum loads) calculation using the upper bound theory of limit analysis. It is interesting to find that no matter what the slope structures and mechanical parameters are, the optimal path of toppling fracture plane is straight and most likely oriented perpendicular to the bedding planes. Hereby, considering structural damage will enable progressive toppling deformation instead of systemic failure, the toppling deformation evolution is probably taking place of a loop following the formation of the first fracture plane due to exceeding slope critical height. In the loop, deformation and column inclination updates due to fracture plane formation and fracture plane inclination increase to adjust the changed inclination of columns, as it may take degrees perpendicular to columns. And this progressive formation of ever more inclined fractures plane is what lead to sliding collapse. Altogether we divide the toppling evolution into 5 stages, and define the instability criterion for toppling deformation transform into sliding collapse as the fracture plane inclination 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 toppling slopes 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 could lay a foundation for the deformation, stability and early-warning analysis of toppling slopes.