Page 586 - Rock Mechanics For Underground Mining

Appendix A Basic constructions using the
hemispherical projection

A.1 Projection of a line

The construction described here is used to represent the orientations in space of lines
such as the normals to planes or force vectors. The orientation of a line in space is
represented by its trend and plunge.
◦
The plunge of the line, (−90 ≤ ≤ 90 ), is the acute angle, measured in a
◦
vertical plane, between the line and the horizontal. A line directed in a downward
sense has a positive plunge; a line directed upwards has a negative plunge.
The trend of the line, (0 ≤ ≤ 360 ), is the azimuth, measured by clockwise
◦
◦
rotation from north, of the vertical plane containing the line. The trend is measured in
the direction of the plunge. Thus the downwards directed and upwards directed ends
◦
of a line have trends that differ by 180 .
The trend and plunge of a line are analogous to the dip direction and dip of a plane.
They are also represented by a three-digit number (trend) and a two-digit number
(plunge) separated by a slash, e.g. 045/73.
The following steps are used to plot the equatorial or meridional projection of a
line:

(1) Locate a piece of tracing paper over the meridional net (Figure 3.24) by means
of a centre pin. Mark the north point and the centre and circumference of the net
on the tracing paper. When a large number of stereographic analyses are to be
carried out, it is useful to prepare several sheets of tracing paper on which the
north point and the centre and circumference of the circle have been marked.
(2) Using the gradations around the perimeter of the net, mark the azimuth corre-
sponding to the trend of the line. (This procedure is illustrated in Figure A.1a
for the comparable case of the dip direction of a plane.)
(3) Rotate the tracing paper about the centre pin until this mark lies on the east–west
diameter of the net.
(4) Count from the perimeter of the net, along the diameter, the required plunge
angle. Mark and label the point using some convenient notation.
(5) Rotate the tracing paper so that the north point is returned to its home position.

A.2 Projection of the great circle and pole to a plane

The construction used to plot the equatorial or meridional projections of the great
circle and pole of the plane 130/50 is illustrated in Figure A.1. The following steps
are used:

(1) Locate a piece of tracing paper over the meridional net (Figure 3.24) by means
of a centre pin. Mark the north point and the centre and circumference of the net.
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