The failure of any particular rock slope can involve a number of modes including planar sliding, circular sliding, wedge failure, toppling and some combination of these. While planar, circular and wedge modes have received detailed analytic treatments, the toppling mode has only recently been considered as a potentially significant rock slope failure mode. The different types of toppling as described by Goodman and Bray (1976) are (a) flexural toppling, (b) block toppling and (c) block-flexural toppling. However, some potential secondary toppling modes exist such as (i) slide-toe-toppling, (ii) slide-head-toppling, (iii) slide-base-toppling, (iv) tension-crack toppling, and (v) toppling and slumping. Attempts have been made in this paper to analyze theoretically two of these secondary toppling modes namely: (i) slide-toe-toppling and (ii) slide-head-toppling. Generally, the static stability analysis of rock slopes susceptible to the aforementioned secondary toppling failures, involves the determination of forces generated by the overturning columns of rock higher up on the slope and those generated by resisting columns of rock in its lower portions. These forces are calculated as functions of the heights of rock columns from the base plane (h); the thickness of the rock columns (t); the dip angle of the base plane (d); step angle (a); overall slope angle (¿); block-base friction angle (fb); interblock friction angle (fj) and block-weight-ratios (BWR). Depending on the various ratios of width-to-height (t/h) of the individual blocks and the frictional properties of the interblock and interlayer discontinuities (fj and fb respectively) with respect to the dip of the layers (d), sliding or toppling or a combination of these could occur. Based on the limit equilibrium criterion, factors: of safety with respect to both slide-toe-toppling and slide-head-toppling have been defined as the ratios of the resisting forces to the driving forces. Stability field charts for both the slide-toe-toppling and slide-headtoppling failure mechanisms at various dip angles of bedding plane (d) and frictional characteristics of interblock and block-base surfaces, have been constructed and discussed. Field applications of these secondary toppling failure modes are also discussed. Additionally, the influence of groundwater on the rotational stability of blocks on rock slopes is presented in detail.
Some of the factors of major importance to the stability of rock slopes are the frequency, orientation and shear strength parameters (c and f) of the discontinuities present in the rock mass. Based on these factors, failure of rock slopes could occur in a number of modes. Some of the failure modes frequently observed (Muller, 1964, 1968; Hoek and Bray, 1977; Goodman, 1976, 1980) are (i) plane-sliding failure, (ii) wedge failure and (iii) circular failure. A failure mechanism which has received serious attention in only the last decade is toppling (deFreitas and Watters, 1973; Bukovansky, et al., 1974; Goodman and Bray, 1976; Hittinger, 1978; Hocking, 1978; Zanbak, 1978; Brown, 1982; Teme, 1982 and Teme and West, 1982). Teme, 1982 and Teme and West, 1982). Toppling failure usually occurs in rock masses with closely spaced, near-vertical discontinuities that dip into the cut slope. This situation is shown in Figure 1.