Engineering Rock Mechanics

Questions and answers: design of surface excavations^333

'y

a\,,..**'.

,/'

,,/'

.-'

zero, and will the stress state on the bedding plane to the left of
this point be sustainable? Over what range of x-ordinate values to
the right of this point will slip occur on the bedding plane? What
conclusions can be drawn about the overall stability of the proposed
dam?

I ground surface

6m

bedding plane

A18.9 The forces P and Q are applied to the ground through the
material of the dam, and hence exert normal and shear stresses on
the foundation, rather than line loads. However, in order to make a
preliminary analysis we will assume that these forces are, in fact, applied
to the foundation as line loads.
Although we could find the position of zero radial stress algebraically,
it is both more convenient and instructive to sketch the general form
of the shape of the contours of radial stress (the so-called 'bulbs of
pressure') beneath an inclined line load, and use this to identify an
approximate location for it. This analysis will be approximate because it
does not take into account the direct stress in the radial direction due
to the weight of the rock overlying the bedding plane. The radial stress
contours take the following form:

line o

inrlin

This shows that the position of
zero radial stress is given simply
by the orientation of the line load.
Sketching the geometry of the prob-
lem allows us to evaluate this:
Thus we find that

from which we obtain

• 12.8 m

9400

4400

d=6~--

Q

-I

and hence the x-ordinate of the approximate position of zero radial stress

isx = -12.8 m.

The sketch of the contours of radial stress shows that, in general, the

stress state to the left of this point will not be sustainable due to the pres-

ence of the tensile radial stresses. However, we would need to undertake

a detailed analysis that took into account the vertical stress due to the