1. # How slope angles are generated

The slope angles (Figure 1) are one of the main concerns in the mining industry due to security, and all the operational parameters that it can influence. Therefore, this is one of the most important parameters when considering the constraints hierarchy. Usually, it can vary based on the time frames (short/long-term), rock type, lithologies, mine sector, depth, geotechnical domains, etc. Thus, it is important to have these assumptions clear to use this parameter wisely following what you are expecting to your project.

The traditional workflow for open-pit optimization, design, and production schedule may incur in a discrepancy between parameters used for the optimization stage and the design parameters. Ramp design and positioning is a common example on a step that will affect the Overall Slope Angle (OSA). This often brings the need for an iterative process of re-optimizing the same scenario based on the pit designed.

MiningMath works with "surface-constrained production scheduling", defining surfaces that describe the group of blocks that should be mined, or not, instead of the "block precedence" method. By this approach each surface has a feasible solution, considering productions required, and each point could be placed be anywhere along the Z-axis. Therefore, this flexibility allows the elevation to be above, below, or matching a block's centroid, which ensures MiningMath's algorithm to control the OSA precisely, with no error, which would have an even higher impact on transition zones.

The following video illustrates how MiningMath's algorithm handles the definition of slope angles, especially in transition zones.

Figure 1: Slope angles defninition

### Note

Technologies based on Lerchs-Grossmann/Pseudoflow approaches also present a broadly-known "slope error" which is the difference between the optimization input parameters for OSA and what is measured from output pit shells. This is a consequence of the "block precedence" methodology, in which calculations are based on connecting the block's centroids, which might not be achievable when considering the block model dimensions. Therefore, the decision is always on mining or not a block entirely, which affects the OSA and might create additional difficulty to generate a pit shell that matches the designed pit.

# 2. Setting up Slope angles

MiningMath allows the user to handle slope angles in two ways: (I) block-by-block definition inside the model; or (II) a default value, applicable to all blocks or to the blocks from (I), for which there is no information on slopes. It is worth mentioning that for multiple variable slope assumptions, you can add several columns, before the importation, named Slope 1, Slope 2, (...), Slope N. Then, on the interface, select the proper information for each scenario, which avoids the back-and-forth to edit the block model several times.

## 2.1. Block by Block field

This field represents the column(s) that has/have been assigned to the slope during the importation, for varying slope angles on each block. This allows a high level of flexibility to use any specific criteria. These possibilities can also comprise bi-dimensional and tri-dimensional variations, beyond linear and non-linear functions (Figure 2).

## 2.2 Default values

On the interface, you have the option of selecting the information field, which will be the main rule for variable slope angles or to select <none> to define a constant value that will be used for the entire model. The "Default value" settled is also when you use a field that has missing information in the column (Figure 3).

# 3. Slope angles in the Short-term

Short-term Planning is a great opportunity to use the same platform that the strategic mine planning team is using, which allows the company to enhance the adherence/reconciliation of projects by choosing a surface and using it as force and restrict mining to refine everything inside it.

The approach could consider a surface already designed with ramps or any other from MiningMath which respects the Overall Slope Angle (Figure 4) in the time frame required, so that you could use the steeper Bench Face Angles based on the operational parameters of blasting. To use such a feature apply the item 2.2. suggestion and play with different angles accordingly with your project capabilities, this methodology allows you to give flexibility to the algorithm in the constraints hierarchy to find better results.

Figure 4: Operational Bench Face Anlgle and Overall Slope Angle difference.