Engineering Rock Mechanics

Questions and answers: underground excavation instability mechanisms 347

Intersection Orientation Intersection Orientation Intersection Orientation

12 119134 23 191170 34 214120

14 126/27 25 268/39

15 029/50 45 246/02

(2) For each block already identified as being unstable due to sliding,

write down the candidate sliding directions and their orientations.

The most steeply dipping of these is the sliding direction.

The candidate sliding directions, together with the critical direction,

are given in the table below. Note that only block 134 has three

candidate planes for plane sliding, and that blocks 124 and 135 have

none: this reflects the fact that the line of maximum dip of a plane

can only be the candidate for a sliding direction if it is located on the

spherical triangle representing the block.

13 049154 24 114/24 35 044/37

d3 150181

d4 160132

Intersections Critical

419.3 For the unstable roof blocks established in the answer to
419.1, determine the volume of the largest block that could fall
from the roof and hence calculate the necessary suppoH pressure to
ensure stability.

A19.3 Four blocks - 125, 145,235 and 345 - have been identified as
falling from the roof. We need to draw each of these to scale in order
to determine their volumes, which requires the plan traces of the lines
of intersection that make up their roof edges. In addition, we need the
orientations of these lines of intersection in order to compute the block
volumes. For the blocks listed above, we need intersections 12,14,15,23,
25,34,35, and 45.
(1) For all of the required intersections, idenw and label each one on the
projection and determine its orientation. Then draw a radial dotted
line from each one to the periphery. The intersections are as follows:

112 I1 4 115 123 125 I34 I35 14s

119134 126127 029150 191170 268139 214120 04/37 246102

(2) For each plane that forms a block face, draw its strike on the

projection, using a dashed line.

(3) For each block in turn, draw a pair of lines representing the boundary

edges of the roof. Within these draw the outline of the face triangle,

using the dashed strike lines plotted on the projection to determine

their trends. Also draw the intersections representing the roof edges,