Analytical solution for the stability analysis of rock slopes against block toppling failure subjected to seismic loads

Toppling is a typical failure mode of rock slopes dominantly controlled by the discontinuities existing in the slopes, which are often encountered in constructions of various geotechnical engineering. This failure has been classified into two principal types, namely block toppling and flexural toppling. This paper concentrates on the former. To provide a guiding significance for the engineering design, the analysis of rock anti-inclined slopes against block toppling failure due to seismic loads is conducted. On the basis of the limit equilibrium method, a general analytical solution of block toppling failure subjected to seismic loads is deduced for the cases that the block slenderness ratio is relatively large. Furthermore, the explicit expressions are given for the conditions when the geometry is simple. Using the analytical solution, the magnitude of the inter-column forces, the location of failure mode transition point and the magnitude of the toe residual sliding force can be determined. Through four typical examples, the effects of seismic loads on the failure mode of rock anti-inclined slopes, the maximum allowable of the line normal to dip for block toppling failure to occur, and the location of failure mode transition point. The results show that the failure mode of rock anti-inclined slopes can be changed by seismic loads, with the increase of the earthquake influence coefficient, the failure mode is gradually changed from the toppling-sliding failure to the overall sliding failure; The maximum normal angle of the steep discontinuities for block toppling failure to occur and the earthquake influence coefficient have direct negative correlation; with increasing the earthquake influence coefficient, the location of failure mode transition point gradually moves on the latter and the range of the sliding toe gradually expands when the toppling-sliding failure occurs.