344 Underground excavation instability mechanisms
A19.1 To solve this question we use hemispherical projection tech-
niques (see Chapter 7 for an illustration of the techniques and note that
a hemispherical projection sheet is included in Appendix B).
(1) Plot the fracture data on the hemispherical projection. Mark a tick
on the periphery at the appropriate azimuth for each of the five
fracture sets, and label them with the fracture set number and the set
orientation.
(2) Draw the great circle for each fracture set in turn, labelling each great
circle with the set number.
(3) Draw a concentric circle representing the friction angle. In this case,
this is a circle 30" in from the periphery. The completed projection is
as follows:
195i70^160132(4) Write down - in ascending numerical order - the identifying code
for each tetrahedral block formed by the fractures, and then examine
each one in turn to determine its kinematic feasibility. If the spher-
ical triangle defining a block contains the vertical direction, then the
block falls. If the spherical triangle lies outside the friction circle, then
the block is stable. All other blocks slide. The result is as follows,
with the blocks shown in the succeeding projections.Block Instability Block Instability Block Instability
123 sliding 234 sliding 345 falling
124 sliding 235 falling
125 sliding 245 sliding
134 sliding
135 sliding
145 falling