Study of the stability against toppling of rock blocks with rounded edges based on analytical and experimental approaches

Abstract

Rounding of edges in rock blocks is a characteristic feature of spheroidal weathering. The objective of this paper is to examine the influence of edge rounding for rectangular prismatic blocks on the mechanical stability of the blocks against toppling at both laboratory and field scales. Equations for computing factors of safety against toppling and sliding for rectangular prismatic blocks resting on inclined surfaces are discussed first. The equations consider the situation of blocks with sharp edges and with assumed circular rounded edges. The analytical formulae show that rounding of the edges does not have influence on the factor of safety against sliding, but has influence on the factor of safety against toppling. In the latter case, the equations that do not account for rounding of the edges are shown to overpredict the stability conditions of the rock blocks against toppling. Results from a series of laboratory tests using a tilt table to estimate the factor of safety at the critical condition for toppling of blocks at laboratory scale are discussed next. The laboratory results show that for rock blocks with rounded edges produced by a process of abrasion in a slake durability machine, an overestimation of up to 30% or more for the factor of safety against toppling is expected when using classical stability formulae that disregard the curvature of the edges. Finally, stability analysis of large natural rock blocks in the field that show spheroidal weathering, confirm the overestimation of stability conditions predicted by the formulae that do not account for the rounding of the edges.