Engineering Rock Mechanics

230 Rock mechunics interactions and rock engineering systems (RES)

ORIENTATION

Measurements of

orientation may be

imprecise and

naccurate in a highly

fractured rock mass

Discontinuities of

small extent may he

unrelated in

orientation to the

major rock mass

structllre

Depending on the

relative scales of the

roughness and the

instrument used for

neasuring orientation,

roughness may be

identified as a spread

of orientations

The frequency of

intersections along

a discontinuity is

given by

A, = HAicosOi

SPACING

If discontinuities in a

set have a finite trace

length then spacing

values will change

when a discontinuity

appears between two

previously adjacent

features

Spacing between

adjacent

discontinuities is not

uniquely defined for

rough surfaces

As two interesting

discontinuity sets

move away from

being orthogonal, so

trace lengths as

exhibited as block

faces will either

increase or reduce

Intersecting

discontinuity sets will

tend to procude trace

lengths in proportion

to their spacing values

EXTENT

Extent of extremely

rough surface (e.g.

stylolites) may be

difficult to assess due

to effective departure

from a plane

If a failure plane is

defined by a series of

non-parallel

intersecting

discontinuities it will

have an effective

iouglmesJ due lo ita

step-like form

Spacing affects the

absolute size of

effective roughness

Extensive

iiscontinuities tend ta

be planar (e.g.

slickensided fault

Plan@

ROUGHNESS

Figure 14.7 Interdependence between discontinuity geometry parameters.

tensors, e.g. permeability and moment of inertia, are symmetrical: this is

due to the basic equilibrium inherent in these quantities. If, now, we

consider the first 2 x 2 matrix shown in Fig. 14.3, this is also symmetrical

because of the commutative properties of addition. Note, however, that

had we chosen to consider subtraction as the binary operator, the off-

diagonal terms would have had the same absolute value, but with different

signs (e.g. 3 - 2 = 1, whereas 2 - 3 = -l), resulting in a skew-symmetric

matrix. The second matrix of Fig. 14.3 is quite clearly asymmetric, because

the influence of discontinuity aperture on water flow is not the same as the

influence of water flow on discontinuity aperture.

Considering further the other matrices we have presented, Fig. 14.4 is

another skew-symmetric matrix, because the condition boxes are reversed

in sign, depending on which shape conversion is being considered. The

symmetry and asymmetry of the 2 x 2 matrices illustrating the stressstrain

relations for elastic and inelastic materials, respectively, are a result of path-

dependency. This is also the case illustrated in Fig. 14.6, where the regression

is different when different parameters are assumed to be the independent

variable. Finally, the 4 x 4 matrix of Fig. 14.7, which shows the interdepen-

dence between discontinuity geometry parameters, is also asymmetric.

Asymmetry of matrices is associated with path-dependency. An

asymmetric matrix is shown in Fig. 14.8: this is an example of a transition

probability matrix for a Markov chain of state changes. A parameter can

have the states A, B or C. Once the parameter is in one of these states, the