Geoscience Reference
In-Depth Information
comminution step. The size lines, for the nominal fragment
sizes d
1
decreasing to d
6
, are shown as the thin lines that
extend beyond the upper and left edges of the nomograph
boundary. When the sample was split the nominal size stayed
the same but the mass decreased resulting in an increase in the
sample variance. This is shown as the thick line from point A
to point B. During the comminution phase the sample mass
stayed the same and the nominal fragment size decreased
resulting in the sample variance dropping from its position
on the larger size line down to a point on a lower size line
corresponding to the nominal fragment size produced from
the comminution cycle. This is shown as the thick line from
point B to point C.
Fig. 5.6
Segregation due to differences in the fragment size (coarse
fragments roll down the pile concentrating themselves at the edge of the
pile while the fine fragments remain near the centre) (Hartmann
1992
)
5.3.4
Sampling Fundamental Error
The fundamental error that occurs during the sampling pro-
tocol is:
5.3.6
Delimitation and Extraction Errors
†
‡
1 1
IH
MM
σ
2
FE
=
−
ˆ
‰
L
Š
‹
These two errors are related in that if one is present, prob-
ably the other one will also occur. Delimitation error is in-
troduced when the shape of the increment selected from the
lot is not appropriate for the type of lot being sampled. It
can be eliminated through proper practices, although how
controlable it is depends on whether the lot is three-, two-, or
one-dimensional. The ideal samples being a uniform sphere,
a cylinder, or two parallel planes, respectively.
Extraction error is introduced when the method used to
obtain the sample is incorrect. Along with the Delimitation
Error, it can be very detrimental to correct sampling.
The errors produced generally have non-zero means and
introduce a bias to the results. After the correct shape of the
increment has been determined its extraction must follow the
centre of gravity rule. This rule states that all fragments with
their centre of gravity inside the increment belong in that in-
crement and all of the fragments with their centre of gravity
outside the increment do not belong.
S2
S1
This error occurs when the sample is split from a large mass,
M
S1
, to a smaller mass, M
S2.
There is no error introduced
during comminuition—the mass of the sample stays the
same and only the particle size is reduced. Over several sam-
ple preparation stages the fundamental error is the sum of the
error variances during the individual stages:
∑
σ
2
=
σ
2
FE
(FE)i
i
2
2
2
= + ++
σσ σ
(FE)1
(FE)2
(FE)n
This is a simple method for calculating the fundamental error
introduced during sample preparation. The nomograph can
thus be used for sampling protocol optimization.
5.3.5
Segregation or Distribution
Heterogeneity
5.3.7
Preparation Error
Segregation is the heterogeneity between groups of frag-
ments within the sample lot. Segregation can occur during
handling of the material once it has been mined or sampled.
This segregation of material in a lot is due to differences in
the fragment size, shape, density, mass, angle of repose, etc.
Figure
5.6
shows an example of segregation and how the ma-
terial properties contribute to the segregation. The sampling
protocol must be designed to remove any influence that the
segregation may have.
As soon as the insitu material is disturbed to the moment
that it is assayed it is possible to introduce a wide range of
possible preparation errors. Due to the non-random nature
of these errors and the long time frame over which they can
occur, it is important to have a good sampling protocol that
outlines handling and preparation of the sample material
so that the samples are representative. The errors can come
from contamination, losses, changes in the chemical compo-
sition, unintentional mistakes, and fraud or sabotage.
