Kinematic analysis of slope instabiliv mechanisms 32 1N-20"Figure 18.8 Example assessment for a slope of orientation 295"/75"-direct
toppling instability.
(b) The dip direction of the slip planes should lie within approximately
220" of the slope. As with plane instability, this is an empirical criterion
and results from the observation that inter-layer slip tends not to occur
when discontinuities occur obliquely to the slope.
From criterion (a), an overlay is required which is constructed from great
circles (representing the plane of the slope) and yet is used with a pole plot
projection (to establish regions of instability associated with the dip of the
discontinuity planes).
In Figs 18.9(a) and (b), we illustrate the construction of the generic
flexural toppling overlay, together with the specific overlay for these
example data. In Fig. 18.9(a), the radial solid line directed to the left is
again taken to be the slope direction and the great circles represent
planes corresponding to both the slope and the friction angle of the
slipping discontinuity planes. Location of the region of instability is
best understood from an analysis of Fig. 18.9(b). The dip angle of the
dotted great circle in Fig. 18.9(b)-representing the slope-is y, and the
complement of this angle (i.e. the angle to the vertical) is 90 - y. Inter-layer
slip will only occur for discontinuities dipping at an angle of 4 greater
than this (the geometrical criterion above), giving a region of instability
outside the solid great circle. Finally, using the second criterion above,
we produce the shaded instability region-for superimposition on pole
Compare the construction of this overlay with that of Fig. 18.2 (plane
instability), and note that, although both overlays are to be superimposed
on pole plots and the direction of the slope dip relative to the overlayplots.