Structure of Rock - Rock Mechanics Based on an Anisotropic Jointed Rock Model - page 29

The measured orientation of discontinuity sets in homogeneous rock units are subject
to scatter and must therefore be evaluated statistically. For this purpose, the angles of
strike and dip of the discontinuities measured during mapping are entered in a polar
equal-area net leading to a pole plot (Fig. 2.30, upper left). According to the so-called
“Schmidt contouring method”, subsequently the poles that are located within 1% of the
area of the polar equal area net are counted (Fig. 2.30, upper right) to determine the
areal density of the poles or discontinuities, respectively, denoted as the “pole density”.
The pole density D is defi ned as the counted number of discontinuities n divided by the
total number of discontinuities m:
(2.6)
Counting of poles can be carried out by means of computer software or simply by using
a square grid placed over the net with side lengths of a tenth of the polar equal-area
net's diameter. With the aid of a counting circle, also having a diameter of a tenth of
the net, the poles and discontinuities, respectively, can be counted by centering the circle
over each node and on each fi eld of the grid. To enable continuous counting over the
boundary of the net a counting bar can be used. As a result, a plot of pole densities is
obtained (Fig. 2.30, center left). On this basis the pole densities are contoured select-
ing several pole density intervals (Fig. 2.30, center right). Thus, the areas of the most
frequent orientations can be identifi ed and the discontinuities can be grouped into dis-
continuity sets by means of a so-called “Schmidt contour diagram” (Fig. 2.30, lower).
When grouping the discontinuities into sets it is important that only discontinuities of
same appearance and rock mechanical relevance are accounted for.
The orientation limits for each set in most cases are identifi ed by eye. This subjective
approach has the advantage of allowing a rating of the particular site with no further
mathematical treatment. Objective probabilistic methods and algorithms for the auto-
matic grouping of discontinuities into sets are reported in literature. For further treat-
ment of this subject see Section 13.9.2.
Stereographic projection is also used for the determination and representation of an-
gles between discontinuities and between line elements or vectors such as lines of dip,
dip vectors and intersection lines of discontinuities (Goodman 1980). Another possible
application of the stereographic projection technique is the representation of measured
principal normal stresses (Section 16.2.1, Fig. 16.6).
Appearance
The appearance of discontinuities is signifi cantly governed by the surface characteris-
tics, which are particularly important with regard to the estimation of shear strength.
Surface profi les of discontinuities are qualitatively described as “stepped”, “undulat-
ing” and “planar” and, at a smaller scale, classifi ed into “rough”, “smooth” and “slick-
ensided” (ISRM 1978e). At the large scale stepped and undulating profi les are often
designated as “uneven”. Discontinuities are referred to as slickensided when their sur-
faces are very smooth in at least one direction because of a relative shear displacement
(Fig. 2.31).