As distinguished from the former types of toppling failure (i.e. flexural, blocky, blocky-flexural and secondary), another type of toppling failure developed in interbedded hard rock and soft rock slope is very common in Three Gorges Reservoir region. Based on discrete element method, the failure process of toppling failure can be summarized as erosion notches → tension cracks → toppling failure → gravitational transport and accumulation. According to the toppling failure mode, the computing formula of factor of safety is deduced by means of the method of geo-mechanics. The results of a typical case study show that the factor of safety of toppling failure decreases with increasing of notch depth. Supposing the erosion rate of notches is 1 mm/yr and toppling failure of the unstable rock occurs at a notch depth of 1.45 m, we can calculate the time required for the unstable rock to topple as 50 years.


Toppling failure is one of the most serious and hazardous instability of rock slopes (de Freitras and Watters 1973; Goodman and Bray 1976; Wang 1981; Ishida et al. 1987; Goodman 1989; Aydan and Kawamoto 1987, 1992; Adhikary et al. 1996, 1997, 2007). Many toppling failures are observed in practice and hence toppling is an important failure mode that requires further attention (Wyllie 1980; Liu et al. 2010). In general, this failure can be classified into four principal types: flexural, blocky, blocky-flexural and secondary (Goodman and Bray 1976). Flexural toppling failure occurs due to bending stresses (Amini et al. 2009).

However, another mode of toppling failure, which mainly developed in interbedded hard rock (i.e. sandstone) and soft rock (i.e. mudstone, shale and limestone) slope is very common in Three Gorges Reservoir region (Chen et al. 2004; Dong et al. 2010). Field investigation indicates that notches of undercut slopes are formed by differential weathering. Furthermore, tension crack on the top surface will occur due to concentration of tensile stress. As result, the unstable rock begins to topple because of momentum unbalance.

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