Toppling mechamism : resolving the question of alignment of slope and discontinuities
P.M. Mauernbrecher, H.R.G.K. Hack · University of Twente Research Information · 2007
The kinematic test for toppling developed by Goodman and Bray (1976) was based on a two dimensional relationship (90°-δ)+φ j<α (where δ =dip of discontinuity, φ j, =friction angle of the discontinuity and, α =slope angle). The steeply dipping discontinuities into a slope, which the relationship describes, must have a strike nearly parallel to the strike of the slope. ‘Nearly’ is defined as up to 30° out of alignment though in the original paper by Goodman and Bray the strike had to be within 10°. By using the expressions for toppling failure and substituting instead for δ the apparent dip δ a (Hack, 1998, Hack et al., 2003) it is shown that the zone for toppling can be much larger than the 30° as stated by Goodman (1989). The relationship is derived in terms of principal stresses and apparent dip. The equation is more akin to a phenomena describing limited flexural slip at the surface of the slope resulting in ‘spalling’ of rock fragments from the slope surface. By making a distinction between toppling resulting from ‘over-turning’and toppling by ‘spalling’ results in the much more limited instability zone on stereographic projections as described by Goodman 1989. It is the spalling thatwould eventually undermine the layering to form ‘leaning columns’ which can topple by ‘over-turning’ as the term ‘topple’ suggests. The slenderness of the columns and the dip of the layering (‘lean of the columns’) would indicate the likelihood of over-turning.