Condition of toppling failure

Toppling failure is the forward rotation (overturning) of columns or slabs of rock about a fixed base. It occurs in steep slopes with closely spaced discontinuities that dip steeply into the slope.

Conditions (Goodman and Bray)

1. Discontinuities dip into the hill: the dip direction of the discontinuity set is opposite to the dip direction of the slope face, $\alpha_p \approx \alpha_f \pm 180^\circ$ (within about $10^\circ$ to $30^\circ$); the strike is nearly parallel to the slope face.
2. Steep dip: the planes dip steeply, with

$$\psi_p \geq (90^\circ - \psi_f) + \phi$$

so that interlayer slip occurs and the layers can flex and rotate. 3. Slender columns: the slabs are thin compared with their height, with a continuous set of cross joints that form the base of the columns. 4. Steep slope face with the toe free to move, and the centre of gravity of each block falling outside its base.

        \  |  |  |  |
         \ |  |  |  |  columns tilt
          \|  |  |  |  out of slope
           \__|__|__|__

Stereonet test (pole plot): the poles of the planes plot on the same side as the slope dip direction (within about $10^\circ$ to $30^\circ$ of it), at a distance of at least $(90^\circ - \psi_f + \phi)$ from the centre, i.e. below the slip-limit great circle that dips at $(\psi_f - \phi)$ in the slope direction.