Site Investigation - Rock Mechanics Based on an Anisotropic Jointed Rock Model - page 394

distributed with regard to their position. A method for estimating the size distribution
of discontinuities from sampled trace lengths of arbitrarily shaped joints using an op-
timizing process in which the sum of square errors of the sampled and calculated trace
length are minimized was proposed by Song (2009).
The derived relationships between the mean trace length and the mean discontinuity
diameter are normally cumbersome, containing special functions or integrals (Tonon
& Chen 2007). However, if circular disk-shaped discontinuities with log-normal distrib-
uted diameters are assumed,

can be calculated as (Weiss 2008)

(13.19)

where σ d is the standard deviation of the discontinuity diameter distribution. The mean

size of a discontinuity plane then is

(13.20)

The statistical evaluation of trace length data with respect to discontinuity size distribu-
tions may be important when using a discrete rock mass model. However, when apply-
ing a homogeneous model, it should be suffi cient to achieve a conservative estimate of
the persistence of the discontinuities. From a practical point of view, it is recommended
to prepare frequency distributions of sampled trace lengths very conservatively, so if
small rock bridges exist between different discontinuity traces, these traces should be
considered as one single persistent trace length (Wittke 1990).

Based on trace length measurements the planar degree of separation κ p of a rock mass

(see Section 2.7.2) can also be estimated, which is an important parameter for the shear
strength of non-persistent discontinuities (Section 3.3.3).

Block Size
The size and shape of rock blocks separated by discontinuities from the surrounding
rock can be a critical parameter for the stability of rock slopes and underground open-
ings (Chapter 11). The maximum block volume determines, for example, the amount
of support of the roof and the sidewalls of a cavern or tunnel. On the other hand, the
mean block volume allows a rough estimate of the representative elementary volume
(REV) of a rock mass according to the homogeneous model. In addition, block size
serves as an input parameter for blasting design in mining (Maerz & Germain 1996).
In most cases, however, block size is diffi cult if not impossible to measure directly since
only two dimensions of an exposed block or partly exposed block are visible.
Block size is often estimated on the basis of indices such as the volumetric joint cut J v ,
the block size index I b and the RQD (ISRM 1978e). However, no quantitative block
size or block size distribution estimates are possible using these parameters (Maerz &
Germain 1996).