Questions 1 8.1- 18.10: design of surface excavations 475

(a) Using kinematic feasibility techniques, determine whether or not

(b) Indicate, in general terms, the design changes required to overcome

conditions exist that could lead to instability in the proposed slopes.

any predicted instability problems.

418.8 A rock slope with a face angle of I+kf is cut into a rock mass
containing a single set of fractures dipping into the slope at an angle 6.
The strength of the fractures is purely frictional. Assume that tan#, 1C.f
and 6 can all be considered as normally distributed variables with the
following parameters:

Variable tan4 llrf B

Mean 0.55 50" 60"

Standard deviation 0.15 5" 10"

Investigate the variability of the factor of safety due to interlayer slip
for this slope, using either standard normal random values obtained
from statistical tables, or values produced by your computer/calculator.
Perform as many trials as you have the patience for (but at least 35).

418.9 A proposed dam will exert a vertical force of 9400 kN/m and a
horizontal force of 4400 kN/m on its horizontal foundation, as shown in
the figure below. At a depth of 6 m below the founding surface there is a
horizontal bedding plane, the strength of which is purely frictional with

= 32". The unit weight of the rock above this plane is 22 kN/m3.

tY

For a polar co-ordinate system, the origin of which coincides with the

rectangular co-ordinate system as shown in the diagram, the components

of radial stress due to a vertical line load P and a horizontal line load Q

may be calculated from u,(p) = (2P sine) /nr and u,(Q) = (2Q cos 0) /nr,

respectively.

At what value of x-ordinate is the radial stress on the bedding plane

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?