# pit optimiser

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• in Surpac Vision

June 2006

Pit Optimiser Surpac Minex Group

• Table of Contents Introduction ................................................................................................................................ 1 Requirements ............................................................................................................................ 1 Objectives .................................................................................................................................. 1 Workflow .................................................................................................................................... 1 Optimisation Theory .................................................................................................................. 2 Data Requirements and Block Model Preparation .................................................................... 7 Exercise 1 - Optimisation........................................................................................................... 8 Exercise 2 - Ore Discounting Factor........................................................................................ 74 Exercise 3 - Assigning Net Values to block model .................................................................. 82

• Introduction Pit optimisation allows us to produce a model for pit design based on a block model with real world constraints. This document introduces the theory behind the pit optimisation process and provides detailed examples using the pit optimisation functions in Surpac Vision.

Requirements Prior to proceeding with this tutorial, you will need:

To have Surpac Vision v5.1 installed The data set accompanying this tutorial Basic knowledge of Surpac string files and editing tools To have completed the Introduction manual To have completed the Block modelling manual

Objectives The objective of this tutorial is to allow you to create an optimised pit model by applying real world conditions to an existing block model.

Workflow The process described in this tutorial is outlined below:

Understand the theory basis of pit optimisation models Perform pit optimisation on an existing block model Apply optimisation using an Ore Discounting factor Apply optimisation by assigning Net Values to the block model

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• Optimisation Theory Overview An optimal pit for a deposit is one that maximises profit and satisfies both cost and slope constraints. Designing an optimal pit is a challenging and complex problem that is difficult to solve. As a result, several mathematical algorithms have been developed to solve this problem in a reasonable time frame. The Pit Optimiser developed by the Surpac Minex Group is based on a variation of the Lerchs Grossman algorithm that was first proposed by Koenigsberg in 1985. The Pit Optimiser works on a block model of the deposit where each block must have a net value that represents the economic value that will be returned if that block is extracted in isolation. The Pit Optimiser then considers each of these blocks in turn to work out which combinations of blocks should be mined in order to return the highest possible total value given mining constraints for a particular sale price. The result is a 3D surface that represents the base / limit of the pit that maximises the total value of the mine and any further extension of the pit will not increase the total return. Requirements Prior to performing the exercises in this chapter, you should:

Be familiar with the basic principles of Surpac Vision. Be familiar with the Block model module and the Geological database module

Pit optimisation works on a block model of the deposit to be mined and the surrounding material. With any block model, only a subset of blocks will actually contain material of sufficient grade to make them worthwhile to mine once they are exposed at the surface. In order to reflect this information, each block must be assigned a value that essentially shows the net cash flow that would result from mining that block in isolation. This value must be positive for an ore block and can be calculated as the sale price minus the costs of mining and milling. For waste and air blocks, this value will be zero or a negative value representing the cost of mining that block. To illustrate this, the diagram below shows a cross section of a deposit. For simplicity, all air blocks in the block model for this ore body will be given a value of \$0, the mining cost associated with extracting an ore or waste block will be set at \$3, while the sale price for each ore block will be \$20.

2

• The diagram below shows a cross section of the block model for this deposit. Each block has been assigned a net value indicating the cost of extracting the block if it were already exposed.

Once all the blocks have been assigned a net value showing the cost of extracting just that block as if it were already exposed, each block is then considered in turn and all the blocks that are needed to be mined in order to uncover it are identified. From these blocks, it is then possible to calculate the total net value of a block in relation to its position in the model. This will be the net value of the block in question minus the cost of mining all the blocks that need to be mined before it can be extracted.

In the above example, we have assumed that in order to mine a block, the block directly above it must be extracted first. Therefore, to calculate the total net value of a block, you would take the net value of the block and subtract the net value for all the blocks above it.

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• After the total net value for each block is calculated, it is then a matter of finding the combination of blocks to extract that will result in the maximum return for that deposit. As shown below, the maximum value for a vertical pit (90 degree slope angle) for this deposit is \$40. This is computed by adding up the total net values of the blocks along the base of the pit outline.

If more blocks were extracted, the total return of the pit would actually decrease as shown below. When an extra column of blocks is extracted, the value of the pit is \$39.

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• Likewise with a smaller pit, the total return is only \$38. This is illustrated below.

An optimal pit is one which returns maximum revenue. A slightly smaller pit will leave revenue on the pit walls, while a slightly bigger pit is unprofitable at its limit. In pit optimisation, wall slope angles are an important consideration when calculating the optimum pit because these angles determine which blocks need to be mined before a certain block can be extracted. This in turn affects the total net value for each block and will result in different blocks forming the optimal pit. The above simplified case assumed a slope angle of 90 degrees which is unrealistic. If on the other hand, a slope angle of 45 degrees is assumed, the following results would be achieved.

The maximum value for a 45 degree slope pit would give a value of \$13 and is once again calculated by adding up all the total net values of the blocks along the base of the optimum pit.

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• Regardless of the slope angle used, a slightly smaller or larger pit would result in less return as shown in the two diagrams below.

As can be seen from the above, finding the optimal pit for a deposit is not a simple process. There are many different combinations and sizes of pit outlines that need to be assessed before it is possible to determine which pit will return the most profit for a given sale price. This process can be repeated by increasing the sale price to calculate more profitable pits closer to the surface that are shorter term (2 to 3 years). In effect, a series of nested pit shells can be produced and used as a rough guide for determining the schedule of the mine or estimating the maximum net present value of the mine. The two algorithms that the Surpac Minex Group pit optimiser uses are the Floating Cone and Lerchs Grossman techniques to determine an optimal pit for a deposit. These two algorithms are discussed later.

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• Data Requirements