Engineering Rock Mechanics

92 Fractures and hemispherical projection

This array is not

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principles of all

The numbers

number of sides of

example polygons

Figure 73 Array of lines illustrating two geometrical principles: there is a relatively large

number of triangular areas compared to the number of other polygons, and there are

more shorter lengths of intact rock intersected by the scanline than longer lengths.

Although the fracture * patterns can appear daunting (as in Fig. 7.2b),

they exist because of definite mechanical and hydraulic principles: it

is this fact that enables structural geologists to interpret their origin.

Also, we have the necessary tools for engineering characterization, i.e.

measurement equipment on site, understanding of the geometrical and

mechanical features, and associated graphical and computer techniques.

Thus, given a fracture array, such as one of those in Fig. 7.2, the

geotechnical engineer wishing to know the frequency and orientation

of the fractures, the mechanical properties of typical fractures and the

mechanical and hydrogeological properties of the whole-rock mass does

have the necessary tools available.

It is helpful to understand aspects of the basic geometry associated

with the rock fracture arrays. Assume that on a sheet of paper 20 straight

lines have been drawn, each at a random orientation, right across the

page (see Fig. 7.3), representing rock fractures. Then assume that a

straight line is drawn at any orientation through the array (the dashed

line in Fig. 7.3), representing a sampling scanline on a fractured rock

exposure or a borehole through a fractured rock mass. We can consider

first all the areas formed by the fracture lines: these are equivalent to

cross-sections through the rock blocks formed by the fractures. Some

areas will be triangles, some quadrilaterals, some five-sided figures, and

so on. It is possible to find the mean number of sides that all the areas

have, both for a specific array and theoretically for all such arrays.

The number of sides of all the closed polygons in the fracture diagram

in Fig. 7.3 was counted and a histogram (Fig. 7.4) prepared.

’ Note. The terms ’fracture’ and ’discontinuity’ are both used to denote the preexisting

bedding planes, faults, shears, joints and fissures in a rock mass. We use the term

’fracture’ without any structural geology or engineering genetic connotations, to indicate

a discontinuity in the mechanical rock continuum. A fracture has little or no tensile

strength. If we are discussing an engineering-induced fracture, rather than a natural

fracture, this will be made clear.