Civil Engineering Reference
In-Depth Information
Toppling failure
9.1 Introduction
The failure modes discussed in the three previous
chapters all relate to sliding of a rock or soil mass
along an existing or induced sliding surface. This
chapter discusses a different failure mode—that
of toppling, which involves rotation of columns
or blocks of rock about a fixed base. Similar to
the plane and wedge failures, the stability analysis
of toppling failures involves, first, carrying out
a kinematic analysis of the structural geology to
identify potential toppling conditions, and then,
if this condition exists, performing a stability
analysis specific to toppling failures.
One of the earliest references to toppling fail-
ures is by Muller (1968) who suggested that block
rotation or toppling may have been a contribut-
ory factor in the failure of the north face of the
Vaiont slide (Figure 9.1). Hofmann (1972) car-
ried out a number of model studies under Muller's
direction to investigate block rotation. Similar
model studies carried out by Ashby (1971), Soto
(1974) and Whyte (1973), while Cundall (1971),
Byrne (1974) and Hammett (1974) who incor-
porated rotational failure modes into computer
analysis of rock mass behavior. Figure 9.2 shows
a computer model of a toppling failure in which
the solid blocks are fixed and the open blocks
are free to move. When the fixed blocks at the
face are removed, the tallest columns of blocks
topple because their center of gravity lies outside
the base. The model illustrates a typical feature
of toppling failures in which the tension cracks
are wider at the top than at the base. This con-
dition, which can best be observed when looking
along strike, is useful in the field identification of
topples.
Papers concerning field studies of toppling fail-
ures include de Freitas and Waters (1973) who
discuss slopes in Britain, and Wyllie (1980) who
demonstrates stabilization measures for toppling
failures related to railway operations.
Most of the discussion that follows in this
chapter is based on a paper by Goodman and
Bray (1976) in which a formal mathematical solu-
tion to a simple toppling problem is shown. This
solution, which is reproduced here, represents
a basis for designing rock slopes in which top-
pling is present, and has been further developed
into a more general design tool (Zanbak, 1983;
Adhikary
et al
., 1997; Bobet, 1999; Sageseta
et al
., 2001).
9.2 Types of toppling failure
Goodman and Bray (1976) have described a
number of different types of toppling failures that
may be encountered in the field, and each is dis-
cussed briefly on the following pages. The import-
ance of distinguishing between types of toppling
is that there are two distinct methods of stability
analysis for toppling failures as described in the
following pages—block and flexural toppling—
and it is necessary to use the appropriate analysis
in design.
9.2.1 Block toppling
As illustrated in Figure 9.3(a), block toppling
occurs when, in strong rock, individual columns
