IMS 1.0
Intelligent Mining Software “Solutions”
IMS - Grade Tonnage Reporting
Produced by W.S. Mart and G. Markey
For MineMap Pty Ltd
Intelligent Mining Software “Solutions” IMS - Grade Tonnage
Reporting
Copyright © 2013 by William Seldon Mart and Geoff Markey. All rights reserved.
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Intelligent Mining Software “Solutions” IMS - Grade Tonnage
Reporting
Table of Contents
INTRODUCTION.................................................................................................................... 4
GRADE TONNAGE REPORTING ....................................................................................... 5
The Calculation Options Page ................................................................................................. 6
The Mining Horizons Page ....................................................................................................... 7
The Mine Plans Page .................................................................................................................. 9
The Region of Volume Page ................................................................................................... 10
The Recovery/ Dilution Page ................................................................................................ 13
The Report Categories Page .................................................................................................. 15
The Mozaic Limits Pages ......................................................................................................... 17
The Mozaic Limits – Allowable Strat Units Page ............................................................ 19
The Mozaic Limits – Inclusion of Waste Strats page ..................................................... 20
The Output Page ........................................................................................................................ 20
The Schedule Output Page ..................................................................................................... 22
APPENDIX A: NOTES ON IN-SITU VOLUME CALCULATIONS .............................. 23
APPENDIX B: NOTES ON CUT AND FILL VOLUME CALCULATIONS................. 24
Introduction........................................................................................................................................... 24
Method of Operation ........................................................................................................................... 24
Reporting ................................................................................................................................................ 25
Cumulative and Incremental Volume Calculations ................................................................. 25
APPENDIX C: NOTES ON VOLUME AND ORE QUALITY CALCULATIONS ....... 26
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Volume Calculation Method ............................................................................................................. 26
Weighting Factors ................................................................................................................................ 26
Importance of a Surface Seam ......................................................................................................... 27
Calculating Volumes for Production Periods............................................................................. 27
Sequential Calculations Using Region Plan Files ...................................................................... 28
Adequate Definition of Mine Plans for Volume Calculations ............................................... 28
Calculation of Volumes for Separate Seam Plies ...................................................................... 28
Accuracy of Volume Calculations ................................................................................................... 29
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INTRODUCTION
Grade tonnage reporting calculates quantities and average qualities of ore, together with
corresponding waste volumes, from a previously generated deposit model.
Mining losses and in-pit dilution are considered in the calculation of all quantities and qualities, where
they are nominated. These parameters and others, such as relative density and nominal waste qualities
(unmodelled), can be specified for the model as a whole or individually for each ore seam or waste
interval.
There are a number of functional subdivisions within grade tonnage reporting and the path taken
through the wizard depends on the method selected and the degree of detail required in the reported
quantities and average qualities.
There are two prime functional subdivisions;
1. In-situ volume calculations
a. Simple volume report calculations
b. Detailed volume report calculations
c. Detailed mozaic volume report calculations
2. Cut and fill volume between two plans.
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GRADE TONNAGE REPORTING
1. Load the relevant model into the 3D View Pane.
2. Select the <Model>< Grade Tonnage Reporting...> menu item (Figure 1) to display the first
page of the grade tonnage reporting wizard.
Figure 1: Selecting the grade tonnage reporting option.
NOTE:
1. The definition must have a model attached for in-situ volume calculations. See the MODEL
DEFINITIONS and BLOCK MODEL OPERATIONS manuals for more information.
2. The definition must use a single stratigraphy for cut and fill volume between two plans.
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The Calculation Options Page
Figure 2: Selecting calculation type and saving working copy
1. Select the calculation type you require (Figure 2).
2. Enter the name of the output model or leave the field blank if an output model is not required.
As long as you do not leave the grade tonnage reporting module, the output model is
incrementally mined out at each pass for successive depths/horizons, plans and regions to
prevent double counting of quantities.
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The Mining Horizons Page
Select the method used to report volumes. The volumes can be reported by elevations or depth.
Report volumes by Elevation
The quantities/qualities are calculated above each horizon specified up to the surface for the first
horizon and up to the previous horizon for each successive horizon (Figure 3).
Figure 3: Reporting volumes by elevation
Report volumes by Depth
The quantities/qualities are calculated above the nominated depths. Depths are taken from the roof of
the top seam present in the model at a given location (Figure 4).
In the case of a mined out model this need not be the natural surface.
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Figure 4: Reporting volumes by depth
NOTES:
1. Quantities/qualities are calculated for each stratigraphic unit and the corresponding
interburden within increments of "elevation" or "depth from surface" as specified.
E.g. if elevations or depths are specified at 25m increments, a separate listing of
quantities/qualities for each stratigraphic unit and corresponding waste is provided for each of
those increments, together with a total.
2. If you only require the total quantities/qualities for ore and waste by stratigraphic unit within
the model area (or limited area specified later), then specify a single elevation below the
lowest point of the bottom stratigraphic unit. This would commonly be the case in a block
model in which the stratigraphic units have been named to correspond with the bench
elevations.
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3. For detailed mosaic volume calculations, a laminar (coal) model would require a number of
input elevations to produce volumes by horizon.
The Mine Plans Page
Figure 5: Specifying the depth
Select one of the four methods to specify the depth to which the model will be mined and volumes
reported (Figure 5).
Mine the entire model
Mine plans will not be used so the grade tonnage reporting will be en masse.
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En masse calculations include all ore and waste present in the model within other limits specified. The
total grade tonnage reporting will be affected by the selections made in the Mining Horizons and the
Region of Volume property pages.
Mine down to one or more triangulations
Specify one or more IMS CAD file that define the surfaces to mine out of the model. Grade tonnage
reporting requires that each file contains a triangulation that can represent a pit design, survey pickup
or natural surface. For best results, each triangulation should cover at least the region selected for the
volume in the Region of Volume property page.
Mine down to contours
Specify one or more IMS CAD files that define the surfaces to mine down to. Each file should contain
strings/polygons that can represent a pit design, survey pickup or natural surface.
When using contours to represent a surface, all strings and polygons in the file will be treated as
contours. To calculate an elevation for a given point the reporter searches from the location of the
point in each of the four cardinal directions (North, South, East and West) until it finds a line segment.
The elevation of each of these segments is calculated at the point of intersection and these four (or
fewer) values are combined into a distance-weighted average. This final value is used as the elevation
of the surface at that point. To calculate a volume down to a contour file, IMS applies this
interpolation for each cell centre and mines the model down to that level. Note that the data does not
need to be true contour data as the interpolation method works on any string data.
NOTES:
1. Cells that are not covered by the contour data may have an elevation calculated if they lie due
North, due South etc of the data. Other cells will be considered to have the datum elevation
stored in the definition. During the four-way search, if even one direction finds a segment, an
elevation is calculated and used therefore you should ensure that your contour file contains
valid data across the entire region of the calculation.
2. Using a contour is slower and less precise than using a triangulation. Additionally, a
triangulation has a clearly defined boundary. In most cases a triangulation is preferred over
contours.
3. If you select multiple files for contours or triangulations then each surface will be considered
in turn, with the input model for one surface representing the portion of the model that
remains after removing material down to the previous surface. Each file will generate a
separate section in the report.
Mine down to the surface of the model
The surface of another model can be used to mine the model. This is particularly useful after running
Lerch-Grossman pit optimization which creates an output model to define the surface of the optimum
pit. This model can be used directly to calculate detailed volumes within this pit.
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The Region of Volume Page
Figure 6: Selecting the plan view and three dimensional limits
1. Choose the type of the plan view limitation and the three dimensional boundary. It may be the
entire mine or lease area, or a block or sub-block within the mining area (Figure 6).
Polygons in an IMS CAD file
Select an IMS CAD plan file containing a single polygon (e.g. a digitised boundary of
horizontal limits.).
String set in an IMS CAD file
Specify the IMS CAD file and the string set name. IMS allows you to generate a set of parallel
polygons or a grid, which you can refer to by name (called a string set). In grade tonnage
reporting, IMS will process each string/polygon identified in the string set as a unique region.
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NOTE:
The elevations of the points in each string or polygon are irrelevant. When a polygon is
processed IMS will look at each cell in the model and determine whether the centre of the
cell is in the polygon. If it is not then the cell is ignored and will not be accumulated in the
report.
Cell range of the model
Specify the row and column range that define the required rectangular area of the model.
2. Select the three dimensional boundary (optional).
You can also select another region defined by a solid in the specified CAD file. This option is
only available for the detailed volume report calculation type.
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The Recovery/ Dilution Page
Figure 7: setting the recovery/ dilution
1. Select the recovery type from a thickness of ore lost in mining (i.e. height loss) or a
percentage of the total (i.e. percent recovery).
2. Select each item in the parameter list and enter the values for that parameter. The values can
be either globally specified or specified by stratigraphy. A description of each parameter
follows:
Recovery/Height loss
This value is applied to all stratigraphic units designated as "Ore" in the model definition (see
the MODEL DEFINITIONS manual). In a coal operation this would indicate how much
coal is lost in each coal seam. In a block model, you would normally indicate no loss by using
100% recovery.
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Total recovery is either 100% or zero height lost. Ore lost is added to the waste stratum above
the ore.
RD
This parameter is only valid if relative density is not modelled. If relative density is modelled
then the modelled data will be used and a statement to that effect will appear.
RD Waste
This option is only relevant for laminar models. This must be supplied (if not modelled) so
that the effect of dilution on ore tonnage can be calculated.
Dilution by waste
Dilution is considered to be waste material removed from the waste stratum below the ore
horizon and added to the floor of an ore horizon (i.e. the volume is subtracted from a lower
waste unit and added to the ore unit). It is always specified as a thickness (height). The default
units are meters.
NOTES:
1. Consider using advanced cropping for very thin/zero thickness seams if you are using
global dilution parameters since dilution will be applied to all seam occurrences
which can over estimate the ‘ore’ seam material. Individually specified parameters
can set a minimum seam thickness before applying dilution.
2. The dilution factor does not operate on the bottom seam. Since the model does not
exist below the last modelled seam/bench, no account is taken of over-mining below
this seam/bench, i.e. the “dilution factor” does not operate. If you want to take
account of dilution from the floor of the bottom bench/ore horizon, you will have to
include a modelled waste seam/bench below the bottom modelled ore horizon.
Otherwise, add a dummy waste stratigraphic unit to the bottom of four drillholes (real
or dummy) in the ASCII file from the drillhole database for that model. This can be at
some arbitrary level below the lowest ore seam/bench at a constant thickness so that
the editing procedure is simplified.
3. Incorporation of lower waste levels also enables excavation in a mine plan below the
lowest ore horizon to be considered, e.g. sumps, etc.
Quality values for interburden or overburden
These values must be supplied so that the effect of dilution on ore quality can be calculated. A
single quality value supplied here for each modelled quality is applied to all waste strata.
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The Report Categories Page
Figure 8: Categorization of report
1. Select an item from the assay list.
2. If the report should use ranges of the selected item then select the check box and enter the
required ranges. There is no need to cover the entire range of a variable in a given model.
The order of input is not important - it will be sorted automatically.
Assays of type “weight by primary material”, “primary material” and “relative density” are calculated
as shown in Equation 1 through Equation 4. This is principally for use in heavy mineral deposits:
E.g. Ilmenite and zircon grades are weighted by the primary material called “heavy mineral”.
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Equation 1: Calculating composite value for Ilmanite.
Equation 2 Calculating composite value for Zircon
Equation 3 Calculating composite value for primary material
Equation 4 Calculating composite value for relative density
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The Mozaic Limits Pages
This page is available only for Detailed Mozaic Volume Reports. These reports are used for laminar
models such as those which may be developed for a coal deposit
Figure 9: Setting the mozaic limits
Minimum and Maximum limits for elevation and depth
The minima and maxima requested are absolute limits to the calculation. If a strata unit in the
sequence is outside these limits at a location then no value is calculated for that location. Use as wide
a range as necessary. Negative numbers are accepted.
Upper and lower stratigraphic units
These define the limiting stratigraphic units to be combined in the calculation. The stratigraphic units
and all intervening units will be combined where all other conditions are satisfied.
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Stratigraphic units to be tested for boundary condition
The stratigraphies specified here must lie in the sequence between the upper and lower stratigraphic
units and within the elevation and depth ranges. If all units lying between the selected parameters are
required then enter the word “TOTAL” without the quotes.
Assay to be tested for mozaics
Select the assays/qualities to be tested for the mozaic.
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The Mozaic Limits – Allowable Strat Units Page
This page is available only for Detailed Mozaic Volume Reports.
Figure 10: Setting the testing limits for strat and assays
Set the minimum and maximum values for each item in the list.
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The Mozaic Limits – Inclusion of Waste Strats page
This page is available only for Detailed Mozaic Volume Reports.
Figure 11: Inclusion of the waste strats
1. Select the required radio button to include all stratigraphy units or to exclude non-assay
stratigraphy units.
2. If all stratigraphies are included then a background assay value can be specified for the unmodelled (or waste) stratigraphic units.
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The Output Page
Figure 12: Nominating output files
1. Enter a name for the text report file or leave it blank to disable text reports. If you specify a file
extension of HTML then the report will be an HTML file which can be viewed in any Web
browser. (E.g. REPORT.RPT is a plain text file but REPORT.HTML is an HTML file.) The
HTML file has richer formatting.
2. Enter names for the Microsoft Excel and CSV types or leave them blank to disable that type of
report.
3. Enter a name for the mined cell output ASCII file or leave it blank if an output file is not required.
4. Select the required check boxes to simply the report.
5. Select the colours for the table header, rows and footer used by Microsoft Excel files.
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The Schedule Output Page
Figure 13: Nominating schedule output files
1. Enter the names for the schedule output files or leave them blank to disable schedule output.
2. Select the required fields to include in the schedule files.
3. Press the <Finish> button to start the calculation process. The time taken for the calculation
of quantities will vary according to the size of the model and the number of increments in
elevation or depth.
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APPENDIX A: NOTES ON IN-SITU VOLUME CALCULATIONS
In-situ volumes are calculated for simple, detailed or mozaic reports. The differences between the
three types of calculation are detailed below.
1. Simple calculations report quantities/qualities for seams as a unit (within other limitations);
detailed and mosaic calculations offer separate reports for increments of thickness or a
modelled quality.
2. A mosaic calculation is a more sophisticated detailed calculation, the difference being that the
mosaic calculation allows regions to be finessed with thickness and the quality of composited
stratigraphic units. In other words, even though a vertical column of cells may reside within a
region boundary, the column may be rejected on the grounds of some thickness or assay
constraint. The whole vertical column is rejected, not just a cell.
3. Detailed calculations use a solid body to delineate a region for the volume reports.
The hierarchy of reporting is as follows:
1.
2.
3.
4.
Region
Plan file
Depth or horizon increment
Thickness or quality/assay increment
Not all categories are required in a given calculation but the maximum number of ore qualities which
can be reported in a single output is limited to seven.
Quantities are reported in cubic metres and tonnes or cubic yards and short tons depending on the
units chosen for the system. Average values of seam qualities are reported as percentages or in their
respective units. Mining losses and in-pit dilution are also reported.
NOTES:
1. The grade tonnage reporting module can have two adjacent modelled seams defined or an
unmodelled interburden seam between one seam and the next modelled seam nominated in
the model definition (see the MODEL DEFINITIONS manual), although the interburden
thickness between the two seams can be zero.
In coal environments you should include relative density in the model if possible since an average
density can skew the tonnage. E.g. since the ‘ash’ assay is measured as a weight percent and the
relative density of ash is much higher than that for coal, the calculation of ore tonnages using an
average relative density for coal will tend to overstate the actual tonnage present.
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APPENDIX B: NOTES ON CUT AND FILL VOLUME CALCULATIONS
Introduction
The method employed to calculate the volume of cut and fill contained within a specified area is
similar to that employed in calculating in-situ quantities of ore and waste, except that it works in
reverse.
Using a single bench model as a base, a mine or topographic plan is superimposed to give a "mined
out" model, which forms the base of the area in question. A second plan is then superimposed and the
difference between the two surfaces is calculated.
You must define the parameters for the cut and fill model in the model definition. This model has a
single stratigraphic unit representing the surface. Only the definition is needed so there is no need to
generate the model itself.
Use the definition for an existing model of the area as a basis for the cut and fill model and modify it
accordingly. Weighting factors, trend plans, etc. can all be deleted or left as is -- they are not taken
into account. Delete all stratigraphic units/benches then include a single unit/bench with a suitable
name. Adjust the base point, rotation, cell dimensions and number of cells to suit your requirements.
Other stratigraphic and assay details are not important.
The difference between the basal (model) surface and the second plan file that defines the new surface
is the volume of cut and fill within the specified horizontal and vertical limits. Any regions that are
mined out are "cut" whilst those regions that have been added are reported as "fill".
Method of Operation
Unlike the in-situ calculations, the cut and fill calculations only require four options to be defined
together with the report format:
1. The output model
2. Mining horizons
If you want to subdivide the volume of the new surface at one or more horizons, specify these
horizons here. Start above the highest elevation on the surface and finish above the lowest
elevation. The volumes will be calculated for each of the increments specified. Note that
volumes are calculated downward (i.e. below a given elevation).
3. Mine plans
A number of mine plan files can be specified but at least two plan files are required, the first
defining the original surface and the second defining the new surface.
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The basal plan can be a mine plan, which is usually the case, but can also be a plan file
containing natural surface topography for the area required, not necessarily limited to that
area.
4. Region of volume
Reporting
Reports include volumes of overburden that are added or subtracted from the previous surface plan for
each increment of elevation specified.
Two output tables are produced, the first being the volumes to the basal plan file from the reference
plane above the deposit and the second being the difference between the two plan files. The first table
is incidental to production of the second which is the required output.
Cumulative and Incremental Volume Calculations
Since a new model is created each time the calculation is performed, cumulative and incremental
volumes for cut and fill are always calculated by applying the respective initial plan and the final plan.
In the case of cumulative volume calculations it is always the final pit plan or natural surface that
defines the initial surface. In the case of incremental volume calculations (i.e. volume added) it is the
new surface plan for the previous period that defines the initial surface.
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APPENDIX C: NOTES ON VOLUME AND ORE QUALITY CALCULATIONS
Volume Calculation Method
IMS inspects each cell of each seam in the model to determine whether the centre of the cell is
contained within the limits of the volume to be calculated. Cells within the area defined for that seam
may have been totally or partially included in a previous volume calculation. As each model cell is
mined out, either totally or to the current elevation or depth increment, IMS flags that cell with the
proportion of the cell volume which has been removed. This is achieved by adjusting the elevation
value at the top of the cell to the new elevation.
For cells on the boundary of the area which are intersected by sloping mine faces as indicated in the
mine plan (if applied), IMS calculates the proportion of each such cell to be included in the total
volume. This is accomplished by calculating the intersection point of the mine face with the vertical
projection of the midpoint of that cell and then determining the respective amount of the total cell
thickness removed (defined as the depth from the top of the cell to that point). That cell is then
flagged as being “mined out” to the elevation calculated. The thickness of a cell is the thickness of the
horizon at that point. For en masse calculations, the limits are vertical and the total cell volume is
always included. IMS then sums the total and partial cells to be included for each seam and/or
horizon.
This method prevents double counting of ore and overburden volumes in sequential volume
calculations. This enables the definition of the limits of the volume to be calculated (overlapping of
previous areas is possible) and ensures correspondence between the totals of component volumes and
the overall volumes for the deposit. Average quality calculations are handled concurrently.
In the horizontal plane, the area of a single cell is the minimum increment in the volume calculation.
This allows a proportionate part of the cell volume to be calculated in the vertical direction according
to whether it is intersected by a mine face and its relationship to that face. This is considered to be the
most accurate and flexible method possible since cell area is adjustable but cell depth is not. Create
block or sub-block models with correspondingly smaller cells as required to improve the resolution
and the accuracy of volume calculations.
If volumes are calculated with respect to a superimposed plan file (mine plan), IMS generates a grid
matrix from the plan file which corresponds 1:1 with the model cell matrix. Values assigned to each
grid element, derived from plan elevation values, are used in the calculation with respect to model cell
elevation values for each seam surface.
Weighting Factors
There are three types of qualities that can be included in block models that affect the weighting of
‘Assay’ class qualities in grade tonnage reporting:
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1. Relative Density (if present in the model) is used primarily to calculate model cell tonnages.
These tonnages are then used to weight the ‘Assay’ qualities when calculating totals for
individual model benches and the ‘grand totals’ at the end of reports.
2. Primary Material refers to a quantity that other assays are referenced to (e.g. heavy mineral
percent). This is a proportion of target minerals in material while the constituent minerals are
described as a proportion of the HM concentrate. This weighting factor allows reporting of
the constituent minerals in amounts relative to the real HM%.
3. Ore Proportion is a special assay used by grade tonnage reporting to revise the tonnages of
model cells. It uses a value between 0 and 1 to represent the amount of the cell that is actually
ore. This in turn modifies the tonnes of ore used to weight the ‘Assay’ qualities in report
totals (by bench or grand totals).
Importance of a Surface Seam
To correctly calculate interburden or overburden for its respective ore seam there must be an upper
limit for the interburden or overburden. If the surface seam has been modelled over the entire model
area there is no problem since this will always limit the calculation. However, if the surface seam is
not present over the entire model area (i.e. it is not extrapolated), then IMS uses the next seam below
the surface that does exist as the upper surface of the model. This is a correct assumption if a mined
out model is being employed but is not correct if the surface seam was never generated at that
location. For this reason, ensure that the surface seam extends over the total model area when the
model is generated.
If neither ore seams nor the surface seam are present at a particular location, this has no effect on
volume calculations.
Calculating Volumes for Production Periods
To calculate the production of ore and waste for a given mine plan (either for forward planning or for
current production) the model of the deposit in total can be modified by superimposing a mine plan on
to the model. This is done using IMS to provide a modified model that represents the total deposit
mined out according to the mine plan used. Volumes of ore and waste are calculated accordingly and
the modified model can be stored for later use.
If the modified model is initially specified during a subsequent run of grade tonnage reporting and
another mine plan is superimposed using all other parameters as before, then the difference between
the volumes calculated in each run is the difference between the mine plans used in each run, i.e. the
production of ore and waste required to progress from one mine plan to the other.
The process can be repeated for as many mine plans as required. For repetitive calculations of this
type, where the model is modified at each step, it is a good idea to specify a different name for each
output model. This precaution can save time in repeating previous calculations if the results of the
next step do not meet your requirements and cannot be corrected.
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This technique can be applied to a number of purposes:
1. In forward mine planning, to provide volumes of ore and waste which correspond to a series
of mine plans which can then be located in time with respect to the mine life or, conversely,
to allow the modification of mine plans to correspond to a given production period.
2. In operational mine planning, to provide ore production available and waste production
required in mining a certain block or blocks of ore or in advancing to a particular face
position.
3. In mine operations reporting, to calculate production of ore and waste over a production
period indicated by mine surveys at the beginning and end of the production period.
A given model configuration can be repeated by applying the initial and final mine plans to the base
model.
Sequential Calculations Using Region Plan Files
If you are performing sequential calculations using region plan files to limit each calculation then
make sure each region intersects the adjacent region. Ensure that there are no gaps between the
regions you have formed; this can be done by snapping to common boundary points of the polygons
being formed.
If a there is a gap between polygons used as regions then there is a possibility that a cell within the
gap may be excluded from the volume calculation.
Adequate Definition of Mine Plans for Volume Calculations
For accurate volume calculations using mines plan there must be sufficient line segment information
in the plan file. Where there are large gaps in the mine plan, either on the floor or on the batters, it is
generally necessary to insert additional lines. It is a simple process to find the required elevations for
the end points and to insert the additional lines.
For additional lines on batters, run the lines from the top to the bottom of the batter. For additional
floor information, run two or more lines at approximately right angles across the floor. Use a separate
line type so that these lines can be excluded from subsequent presentation plots.
A contour plot of the mined out model will also show up any inaccuracies. Use Plan View Publisher
to plot composites of stratigraphic unit or bench roof heights for all benches or horizons.
Calculation of Volumes for Separate Seam Plies
At times it may be necessary to calculate volumes for separate seam plies. (E.g. they are to be mined
separately, for the purposes of quality control, separate products, etc.) This is important when
scheduling the removal of each type of ore.
To do this, each ply for which volumes are required must be nominated separately in the geological
database and the output data file from the drillhole database, and also must be modelled separately. If
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this is done then IMS operates normally on the resultant model and produces the required seam split
quantities and qualities.
Accuracy of Volume Calculations
For practical purposes, provided a reasonably small cell size in relation to the area for volume
calculations has been used to build the deposit model, inaccuracies arising from cell boundaries not
coinciding with the area boundary should not be very significant. This is particularly true for
sequential volume calculations where the model is mined out and no double counting can occur.
However, if you want the generated volumes to be more exact then specify a cell size for the model
build which is an even sub-multiple of the areas you wish to calculate and specify the areas by using
the respective northing and easting lines.
The worst case error possible is for an additional half cell width to be included on all sides of the
defined area for the volume calculation. (There is no error for the total model area or if the area is
defined by cell ranges.) This represents one full cell in both the X and Y directions. This error is
expressed mathematically as follows:
Where
and
are the number of cells in the x- and y-directions of the model.
Equation 5: Proportionate maximum error.
Clearly, accuracy can be minimised as the number of model cells increases. However, use discretion
in choosing the number of cells in a model, balancing required accuracy against time for processing
(which increases dramatically as the number of cells increases).
If mine plans are used in the volume calculation then an additional source of error can be noncompliance of plan line elevations (defining roof and floor of ore seams or benches) with the
modelled elevations of the ore horizons. Such discrepancies arise as the distance between data points
on the bench increases. Plan lines between data points are straight, while the seam/ore structure may
curve up or down.
Use discretion in choosing the number and location of data points on the stratigraphic unit or bench to
be used in plan file creation, so that the accuracy of the plan is acceptable for the purpose at hand.
Short term planning, for examples, requires higher accuracy than long term planning.
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