Site Investigation - Rock Mechanics Based on an Anisotropic Jointed Rock Model - page 387

13.9.2 Mapping Evaluation

Sampling of discontinuities
When evaluating a mapping with respect to discontinuity data it must be taken into
account that discontinuities which run approximately parallel to the mapped surface
will intersect far less frequently than those that intersect the mapped surface with a large
angle. As a consequence, the smaller the angle between the mapped surface and the dis-
continuity the smaller is the probability that the discontinuity will intersect the mapped
surface. Effort should therefore always be made to achieve a non-biased sampling of
discontinuities. This goal can be accomplished by arranging the rock surfaces to be
mapped approximately perpendicular to each discontinuity set. For an exploration adit
a uniform sampling can be achieved for example by an appropriate arrangement of
cross-cuts (Fig. 13.16).
In cases where it is not possible to achieve a uniform sampling of discontinuities,
weighting methods may be applied which allow a non-biased evaluation of disconti-
nuity data. Such methods have been suggested in Terzaghi (1965), Grossmann (1980),
Baecher (1983), Kulatilake & Wu (1984b), Priest (1985) and Priest (1993b).

Discontinuity orientation
Measured orientations of mapped discontinuity data are subject to scatter and should
therefore be evaluated statistically. As described in Section 2.7.2 the starting point for a
statistical evaluation of discontinuity orientations is a Schmidt contour diagram or pole
plot (Fig. 2.30). Using GeoID a pole plot can be directly established from the sampled
data (Fig. 13.22) and subsequently sent to a working group for further evaluation.

The mapped discontinuities should be grouped into sets by eye or by probabilistic meth-
ods and algorithms for automatic grouping. Corresponding methods assuming a pro-
babilistic structure of discontinuity orientation data are provided by Shanley & Mahtab
(1976), Mahtab & Yegulalp (1982), Dershowitz et al. (1996) and Marcotte & Henry
(2002). Other algorithms for the identification of discontinuity sets without assuming a
priori probabilistic models are reported in Harrison (1992), Hammah & Curran (1998),
Hammah & Curran (1999), Hammah & Curran (2000), Sirat & Talbot (2001), Zhou &
Maerz (2002), Klose (2004), Klose et al. (2005) and Jiminez-Rodriguez & Sitar (2006).
After delimiting of the sets, some discontinuities may remain which cannot be assigned
to any set and can be regarded as outliers.
For statistical evaluation, the angles of strike of a discontinuity set may be

described by a two-dimensional probability density function (PDF) f(

α and dip β

). In literature
a number of corresponding functions have been suggested including Fisher and Bing-
ham distributions (Watson 1966, Mardia 1972, Kelker & Langenberg 1976, Einstein &
Baecher 1983, Priest 1993a, Priest 1993b). However, Einstein & Baecher (1983) found
that there is no particular PDF with which orientation data can be generally described.
In a simplifying approach also adopted by Zanbak (1977)

α , β

of a discontinuity
set can be assumed to be statistically independent random variables (Wittke 1990). The
two-dimensional PDF f(

α and β

α , β ) then can be expressed by