Use block maths to assign the net value of each block in the model based on gold grade cutoffs.
The cutoff and sale prices that will be used are shown in the following table:
Gold Grade Range (g/t) Sale Price ($/t)
1 – 1.3 16
1.3 – 1.5 18
> 1.5 20
In addition, the cost of extracting both ore and waste blocks is $5/t.
You will now generate an optimal pit where the maximum allowable slope angle is 30 degrees for the entire pit except for the southern region where the maximum allowable slope is 40 degrees.
Open the block model gold.mdl if it is not already open.
A new attribute must be added to the model to store the net value for each block.
From the Block model menu, Select Attributes, then New, to create a float attribute as follows:
The background value for the net value has been set to -5 to indicate that the cost of mining a block (whether it is ore or waste) is $5/tonne.
From the Block model menu, select Save, to save the block model so that it remembers the new attribute.
The next step is to incorporate the sale price into the net_value attribute for all the ore blocks in the model.
From the Block model menu, select Attributes, then Maths.
The first mathematical assignment that will be assigned will be the sale price of $16/t for any blocks with a gold grade between 1.0g – 1.3g. Enter the following function into the Attributes – Maths form:
Press Apply on this form to display the block model constraints form. The following constraints are to be applied:
Press Apply on this form to assign the net value for all blocks with a gold grade between 1.0g – 1.3g.
From the Block model menu, select Save to save the new net_value assignment. A confirmation form will appear, press Yes to proceed.
Verify that the maths assignment worked. From the Block model menu, select Display, then Display Block Model. From the Block model menu, select Constraints, then New Graphical Constraints and enter the following:
Only the blocks with a gold grade range between 1.0g – 1.3g will be displayed as these will be the only blocks that now have a net value of greater than the default value of -5.
The reason why the constraint net_value > 0 was used above is because when assigning net values, all ore blocks must have a positive net value (profitable to mine) while waste blocks must have a negative net value (cost incurred to mine).
The following image should be displayed on your screen:
For extra verification, lets colour the blocks to make sure only the blocks within the gold grade range 1.0g – 1.3g are displayed in this constraint.
From the Block model menu, Select Display – Colour Model By Attribute from the block model menu and enter in the following information:
You should see by rotating the block model around that all the blocks displayed should be coloured in blue. This is shown below:
Now we will assign the net value for any blocks with a gold grade range between 1.3g – 1.5g. The sale price for these blocks is $18/t.
From the Block model menu, select Attributes, then Maths, and fill out the form as shown below:
Press Apply on this form to display the constraints form.
Fill out the form as shown below.
Press Apply on the constraints form to perform the mathematical operation.
After the operation, make sure you save the model otherwise the results will be lost the next time you open the model. To do this, select save from the block model menu and press Yes on the confirmation form that pops up.
To graphically verify that the above operation worked, remove all the previous constraints from the screen .
From the Block model menu, select Constraints, then Remove all graphical constraints.
From the Block model menu, select Constraints, then New Graphical Constraints and enter the following to add new constraints.
Press Apply on the constraints form and only blocks that have a net value of greater than zero (and therefore are ore blocks) and with a gold grade between 1.3g – 1.5g will be displayed. This means the mathematical operation was successful. If the operation was unsuccessful, no blocks would have been displayed on the screen.
Now for the last mathematical operation that will be applied. All blocks with a gold grade of greater than 1.5g will be given a sale price of $20/t.
From the Block model menu, select Attributes, then Maths, and fill out the form as shown below.
Press Apply on this form to display the constraints form. Enter in the constraints as shown below:
Apply the constraints form to proceed and then select Save from the block model menu to save the new net values for the blocks with a gold grade of greater than 1.5g.
Press Yes on the confirmation form that pops up.
Now that we have a net value attribute stored in the model that takes into account mining costs and sale prices of the blocks in the model, we can start entering the parameters for the
optimisation.
From the Block model menu, select Pit Optimisation, to display the Pit Optimisation form. We will create a new parameter file for this exercise.
Press Apply to display the Pit Optimisation Parameters form.
We must now fill out the Ore Type tab pane.
Select $/mass from the Method combo box. We are selecting this method because the net_value attribute that we just set up is expressed in $/t ($/mass unit).
As with the previous two exercises, we will select the ore_type attribute for the Ore Type field to describe which areas of the model are to be considered as the same material.
Note that the ore_type attribute has assigned all the blocks in the model to be of the same material.
Select the net_value attribute that we created during the first exercise for the Net Value Attribute field.
This attribute tells the Pit Optimiser which blocks are ore blocks (positive net values) and which blocks are waste blocks (negative net values).
These are the only fields that need to be filled in this tab because the table on the Ore Type tab pane only needs to be filled in if an attribute for the SG (Optional) field is not chosen.
Click on the Mining Costs tab pane to display the form below:
There is no need to enter any information in the Mining Costs tab pane because the mining costs must already be taken into account in the net value attribute that was chosen on the Ore Type tab pane.
Now click on the Slopes tab pane so we can define the maximum slope constraints for the resultant optimal pits.
For this exercise we will select a maximum default slope angle of 30 degrees. Enter in a value of 30 in the default row of the Default column in the table.
This time we will add in an extra criterion that a maximum slope angle of 40 degrees is to be used in the southern region of the pit.
To enter this information, left click the mouse into the field called South East and change the current value of 30 to 40. Do the same for the field labelled South and South West.
Once the maximum slope angles of the resultant pit have been established, click on the Vertical Limits tab pane.
As we are working with the same data set as the previous exercises, the vertical limits will be the same.
Select topo1.str for the topography location and limit the base by an elevation of 0.0.
Click on the Optimisation tab pane to determine how the optimisation will find a solution.
Once again, select the Lerchs Grossman algorithm to perform the optimisation.
Check the Lerchs Grossman checkbox and leave the Major Cycles field at 0 so the optimisation runs to completion.
A report name must be entered to save a summary of the resultant optimum pit volume and net value.
For this exercise, we will save the report to a Surpac note file called pit_$mass_report.not. To do this, enter the file name pit_$mass_report into the Output Report File Name field and select .not from the Output Report File Format combo box.
Finally, we will save the resultant DTM pit shell that will be created to a file called
pit_$mass0.dtm. Remember that the Discount % is automatically appended to the Output Pit Location name. We also graphically display the result in a layer called pit_$mass and the pit shell will be coloured in cyan.
There is no need to enter in an attribute name for the Value Attribute field above because we manually calculated the net value for each block at the start of the exercise and so, we already have the net value stored in the model.
Note:
With the $/mass and $/volume methods, you cannot enter in discount percentages to affect the sale price of the ore. The reason for this is that the sale price has been incorporated into the net value that we assigned at the beginning of the exercise. Therefore the Pit Optimiser does not know the sale price of the ore to be able to apply discount factors.
Press Apply on the Pit Optimisation Parameters form to run the optimisation The resultant optimal pit shell should appear in graphics as shown below:
By displaying the block model and constraining the pit to show only the blocks with a gold grade value of greater than one (only blocks with a grade value of greater than one were given a sale price), we will be able to see which ore blocks should be mined to maximise profit.
From the Block Model menu, select Display, then Display block model, to display the entire model. Apply the drawing defaults shown below:
From the Block model menu, select Constraints, then New Graphical Constraints and enter the following to add new constraints.
The graphical constraint should appear as follows:
From the Block model menu, select Block model then Report, and fill in the form to find out the tonnage and average grade for gold in the optimal pit.
Press Apply on this form to display the Block Model Report form.
Fill in the form as shown below:
Press Apply on this form and constrain the report firstly by only considering all the blocks above the optimum pit shell:
Secondly, only report on the ore blocks in the model:
After applying the above constraints, the following report should be generated. The volume and tonnage is reported by 20 m benches:
Z Volume Tonnes Gold
Grand Total 249125 597900 2.27
Report
The following report will be generated in the window that pops up:
Results:
Discount Volume Value Output
0.00 552,000.00 6,463,950.00 pit_$mass0.dtm
This shows the volume of the optimal pit is 552,000 m3 and the net value of the pit is
$6,463,950.00This report is saved to a file called pit_$mass_report.not.
Alternative way of getting bench reports – available from Surpac version 5.2 onwards Reset Graphics to clear the graphics view port.
Use the same block model that you have saved the net value attribute that takes into account mining costs and sale prices.
From the Block model menu, select Pit Optimisation, to display the Pit Optimisation form and use the parameter file gold_$mass.pop that was created for the above exercise.
Click on the Report tab and fill it in as shown below:
Results:
Discount Volume Value Output
0.00 552,000.00 6,463,950.00 pit_$mass0.dtm
Bench
0.00 0.00 0.00 11,840.00 4,000.00 130,240.00 1.00 0.00
150.00 -
34,418.75 12,000.00 405,425.00 1.61 1.33
210.00 -
Total pit 589,251.25 250,000.00 -2,612,440.
00
850,171.25 302,000.00 9,076,390.
00
1.92 0.83
Note: Even though you can get a quick bench report, by the optimiser Reports tab, it is not as versatile as the Block Model Reporting. For example you can not specify constraints,/or the number of decimal places to use when reporting.
Pit Attribute
From the Block model menu, select Constraints, then Remove all graphical constraints, to view all the blocks in the model that are in the optimal pit. The entire model will be redisplayed.
From the Block model menu, select Constraints, then New Graphical Constraints and enter the following to add new constraints.
This will show all the blocks within the optimal pit as shown below:
Rotated Block Models
The pit optimiser is only able to handle rotated models around the Z axis only. That is, a model where the bearing has been set to something other than 0. It will not deal with a plunged or dipped model.