Engineering Rock Mechanics

1 28 Discontinuities

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  Random spacing, Random spacing,

  
  


• random orientation orthogonal sets


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0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

a

Figure 7.14 Probability density functions of rock block area sizes for rock masses

containing random discontinuities and two orthogonal sets.

or pole to represent a discontinuity does assume that it is a perfect plane
but that the type of clustering shown in Fig. 7.13 could occur from many
measurements made on an undulating surface.
The word persistence refers to the lateral extent of a discontinuity plane,
either the overall dimensions of the plane, or whether it contains 'rock
bridges'. In practice, the persistence is almost always measured by the one-
dimensional extent of the trace lengths as exposed on rock faces. This is
illustrated in Fig. 7.15. It is clear from this figure that no direct estimation
of persistence is possible from borehole core, although geological inference
based on the type of discontinuity observed is possible. Also, the
distribution of trace lengths obtained from measurements made on an
exposure will depend to a great extent on the orientation of the rock face,
on the associated orientation of the scanline, and whether the measure-
ments are either truncated (values below a certain length are omitted) or
censored (large values are either unobtainable because of limited rock
exposure or because of equipment limitations).
In practice, truncation and censorship always occur, contributing to the
bias in the measurements. For example, there has been considerable
discussion in the literature as to whether the distribution of trace lengths
has a similar negative exponential distribution to that of spacings
discussed earlier, or is a log-normal distribution. It is likely that some of the
differences have arisen from trace length sampling bias, but further work
is needed to clarify the situation. At the moment, there is no clear and
coherent method of measuring trace length, despite its crucial importance.
The word 'roughness' is used to denote the deviation of a discontinuity
surface from perfect planarity, which can rapidly become a complex
mathematical procedure utilizing three-dimensional surface characteriza-
tion techniques, whether these be by polynomials, Fourier series, noise