Engineering Rock Mechanics

348 Underground excavation instability mechanisms

using the dotted intersection lines on the projection to determine
their trends. The three roof lines should meet at a point: if they do
not, your drawing is not accurate enough.
(4) Measure the length of the three face lines and the three roof edges.
Compute the included angle at each face apex using the dip direc-
tions of the fractures that make up the roof planes, and write down
the dip angle of each roof edge. Using these results, compute the area
of the face triangle, the height of the block and hence its weight and
the average support pressure.
(5) The results of the calculations for these blocks are shown in the series
of diagrams below. From these we see that block 235 is the largest, at
2616 kN, and that the support pressure required to ensure stability of
the various falling blocks is 53.3 kN/m2.
It is worthwhile comparing the weight of each block with the size of
the block's spherical tiangle on the projection: this clearly shows that
there is no relation between the two, and hence block weight cannot be
estimated by studying the projection alone. Note also that, for blocks that
deviate widely from a regular tetrahedron, the three individual values
of face area and height are liable to differ markedly. This is an inherent
problem with the technique, caused by the difficulty of drawing the
blocks and scaling the measurements sufficiently accurately. For critical
work, a computational method must be used.

Angles taken from the hemispher-

ical projection:

eI2 = lal - a21 = 1058 - 1951 = 137

es- = las - al I = 1335 - 0581 = 277

812 = 34

825 =39

Psi = 50

0225 = la2 - =^1195 -^3351 =^140

Scale drawing of block (original scale

Block (^125 5) mm: 1 m):