Civil Engineering Reference
In-Depth Information
(a)
(b)
(c)
N
Strike
Strike
N45
°
E
N
North
Dip
direction
Trend
Plunge
W
E
Dip direction
135
°
Dip=50
°
S
Figure 2.4
Terminology defining discontinuity orientation: (a) isometric view of plane (dip and dip direction);
(b) plan view of plane; (c) isometric view of line (plunge and trend).
apparent dip of a plane. True dip is the steepest
dip of the plane, and is always steeper than the
apparent dip. The true dip can be found as fol-
lows. If a pebble or a stream of water is run down
the plane, it will always fall in a direction that cor-
responds to the dip direction; the dip of this line
is the true dip.
planes, and points can represent lines. An
important limitation of stereographic projections
is that they consider only angular relationships
between lines and planes, and do not represent
the position or size of the feature.
The stereographic projection consists of a ref-
erence sphere in which its equatorial plane is
horizontal, and its orientation is fixed relative to
north (Figure 2.5). Planes and lines with a specific
plunge and trend are positioned in an imagin-
ary sense so that the axis of the feature passes
through the center of the reference sphere. The
intersection of the feature with the lower half of
the reference sphere defines a unique line on the
surface of the reference hemisphere. For a plane,
this intersection with the reference sphere is a cir-
cular arc called a great circle, while for a line, the
intersection with the reference sphere is a point.
In order to develop a stereographic projection of
a plane or line, the intersection with the reference
sphere is rotated down to a horizontal surface at
the base of the sphere (Figure 2.6). The rotated
lines and points are unique locations on the ste-
reonet that represent the dip (plunge) and dip
direction (trend) of the feature. In slope stabil-
ity analysis using stereonets, planes are used to
represent both discontinuities and slope faces.
An alternative means of representing the ori-
entation of a plane is the pole to the plane
(Figure 2.6(a)). The pole is the point on the sur-
face of the reference sphere that is pierced by a
radial line in a direction normal to the plane. The
2.5 Stereographic analysis of structural
geology
Previous sections describe structural geological
features that influence rock slope stability. This
data often occurs in three dimensions with a
degree of natural scatter, and in order to be able to
use the data in design, it is necessary to have avail-
able an analysis technique that can address these
matters. It has been found that the stereographic
projection is an ideal tool for this application.
This section describes methods of analyzing
structural geology data using the stereonet to
identify discontinuity sets,
and examine their
influence on slope stability.
2.5.1 Stereographic projection
The stereographic projection allows the three-
dimensional orientation data to be represented
and analyzed in two dimensions. Stereographic
presentations remove one dimension from con-
sideration so that lines or points can represent
