440 Questions 7 0. 7 - 7 0.7 0: anisotropy and inhomogeneity
On the basis of these data alone, is there sufficient evidence to conclude
that the sampling squares should be regarded as different structural
domains?
470.9 The following list of fracture locations, quoted in metres, is taken
from the fracture log of a borehole core which transects a well known
stratigraphic boundary between two units of limestone. Evidently, this
boundary is clear to sedimentologists, but not to geotechnical engineers.
5.780, 6.391, 6.761, 7.105, 7.180, 7.401, 7.478, 8.142, 8.455, 9.139, 10.072,
10.264,10.470, 10.539,10.678,11.421, 11.541, 12.178,12.596,12.620,12.736,
12.936, 13.134, 13.325, 13.430
Use the concept of moving averages to help locate this boundary.
Q 70.7 0 The subject of geostatistics deals with the variation of property
values in space, and so anisotropy and inhomogeneity can be quantit-
atively studied. The basic device of geostatistics is the semi-variogram,
defined as
,_\ n
y = (&) [P (XI - p (x + h)I2
i=l
where y (h) is the semi-variogram statistic for samples distance h apart, n
is the number of sample pairs, p(x) is the rock property value at location
x, and p(x + h) is the value at location x + h.
Using this statistic, a graph can be constructed of y(h) versus h to
indicate the variation in rock property values as a function of distance
between the observations.
YW. .. Si!! .........
1 p:”-pf>+
Case (i) Case (ii) Case (iii) Case (iv)
ie
h h k k
In the diagram above, there are four examples of such semi-variogram
curves for a rock mass. In each case, the length of the h axis represents
50 m.
(a) Explain what type of variation in rock property values, or inhomo-
geneity, each type of semi-variogram represents.
(b) For each type of semi-variogram behaviour, how far away from a
borehole would you feel confident in extrapolating results obtained from
a borehole core?