Geoscience Reference
In-Depth Information
that minimizes the expected loss. In grade control, the
expected conditional loss is a step function whose value
depends on the operating costs (Isaaks
1990
). This im-
plies that the expected conditional loss depends only
on the
classification
of the estimate
z
*
(
x
), not on the
estimated value itself. For example, the loss incurred
when a block of leach ore is sent to the mill is a func-
tion of the difference in processing costs related to both
leach and mill; it will, of course, also depend on the
true block grade,
but not on the
estimated block grade
value itself.
mine. Issues related to material accounting, particularly vol-
umes or tonnages extracted and mine-to-mill reconciliations
are among the most important. As argued in Chap. 11, they
can also be the basis for model performance evaluations.
Operational details, sometimes seemingly trivial, can have
a significant impact on the bottom line. Without pretending
to be exhaustive, some illustrative examples mostly appli-
cable to open pit mines are:
• Sufficient laboratory capacity to provide the assays'
results in the required amount of time, usually 24 h or less
for 200 to 300 samples or more;
• Traffic and destination control in the pit, particularly if
truck dispatch systems are not available; in areas where
manual labor is relative cheap, it is common practice to
place an individual at the pit exit to verify that trucks go
to the correct destination;
• Truck weighing, as a control to truck factors and volumet-
ric measurements;
• If visual indicators of ore are available (such as green
or blue oxide Cu minerals), mine geologists should visit
daily the waste dumps, to ensure that the operation is not
misplacing the ore loads; also, a 24-h operation should
have adequate artificial lighting in the pit, more so when
visual aids are used in grade control.
• The amount of broken ore in the pit should be sufficient to
feed the mill for a few days; an operation where loading is
always pressuring for more blasting goes counter to good
grade control practices.
• Confirm the in-situ bulk density of material loaded;
the operation should monitor in situ density variations,
sometimes taking bulk samples from the pit. Also, con-
sider the estimate of humidity in the rock, which is gen-
erally a simple global estimate. These estimated values
affect the conversion of volumes into tonnages, with a
direct impact in the accounting of metal moved.
13.4.2
Multivariate Cases
Grade control in the presence of multiple variables intro-
duces additional challenges that can be easily handled. The
Ujina open pit example briefly discussed above is in fact a
multivariate grade control issue. There are multiple variables
that add to the value of each parcel of material (copper and
molybdenum), and also multiple variables that detract from
its worth, such as Arsenic or the presence of clays. The mul-
tiple variables can all be mine products, or a combination
of mine products, metallurgical performance variables, and
contaminants in general.
In cases where there are spatial relationships between
the variables of interest, then either co-estimation or co-
simulation (Chaps. 8-10) can be performed. This is most
important when simulating for grade control, since modeling
relationships among different variables is consequential. In
Chap. 14 two multivariate simulation case studies are pre-
sented.
13.5
Practical and Operational Aspects
of Grade Control
Semi-Automatic Dig Lines Definition
A computational
algorithm can be used to develop semi-automatically dig
lines (Neufeld et al.
2005
). While it is unlikely that all issues
will be solved, always presenting the optimal solution, the
process of defining dig lines can be sped up. It is expected,
though, that a degree of manual intervention and validation
will always be required.
The process of automatically defining dig limits is
based on pre-defined operational and selection criteria.
Figure
13.10
shows two cases for dig limits. The model used
to define the ore/waste selection panels is the same in both
cases; the difference is how much one dig limit considers the
ability of the mining equipment to mine to the exact limits
defined.
The optimal dig limits can be posed as an optimization
problem. Sequential annealing (see Chap. 10) can be applied
by defining the objective function as:
There are many operational aspects that need to be considered
for an effective grade control. The most important are (a) the
relationships between the grade control activity and mine plan-
ning; (b) the practicality of obtaining representative samples;
(c) time constraints, always present in any operation; the daily
production target is the operation's main driver which does not
allow for detailed modeling and planning work; (d) the gath-
ering and use of geologic data; (e) the appropriate staking of
the ore/waste zones; (f) the control of the mining process; (g)
the destination of each truck or load of material; and (h) the
accounting of material movement and overall reconciliations.
Each one of the aspects mentioned deserves detailed dis-
cussions and are outside the scope of this topic. However,
they are highlighted here to remind the reader that adequate
grade control involves multiple areas of an operation, and
cannot be developed in isolation from other aspects of the
