1. # Introduction

MiningMath allows the user to combine Force and Restrict mining by using surfaces on each field as you already read in the previous pages. These features allow us to use different arrangements due to concession rights, exchanging of land with adjacent mining companies, allocation of waste material inside exhausted areas, environmental issues, and so forth.

By using them together, the user can either reach the exact shape of a pit if you input the same surface as Force and Restrict mining at the same time frame (Figure 1), which has the highest priority constraint in the hierarchy order. It is also possible to optimize the material between surfaces if you add different surfaces in these two fields (Figure 2), which might be adjusted either to correct the overall slope angle or to increase the NPV, as mentioned before.

Based on these concepts, MiningMath allows you to export surfaces from the best scenario to a bigger mining package, design it with your mining package, create the grid of points, import the designed pit, and, finally, optimize and refine as much as you can by using smart constraints. Therefore, the user has the advantage to control the results by guiding results accordingly with the project requirements.

Figure 1: Using the same surface as Force and Restrict mining to reach an exact shape.
Figure 2: Using different surfaces on Force and Restrict mining to optimize a volume within its limits.

# 2. Practical examples

Surfaces used simultaneously in both fields, force and restrict mining, are interpreted as follows:

• Different surfaces: MiningMath will force mining according to the forcing-surface and will restrict mining according to the restricting-surface.

• Same surface: MiningMath will achieve the same format proposed by the surface in use until the end of the time frame in which they have been applied.

## 2.1. Different surface example

This approach allows you to use different surfaces in the same time frame or split them accordingly to the goals that you want to achieve since this feature works close to what is shown in Figure 2 above.

In this example, it was used the same constraints were mentioned on the schedule optimization page. Besides, the surface 2 of this scenario was add on the force mining field in the second time frame, which means that by the end of the second period the mining should reach at least the shape imposed. The restricting surface used came from the constraints validation page and was added on the last interval, which means that the algorithm could not surpass this limit. Figure 3 discloses the optimized mining sequence volume between the surfaces inserted, and Figure 4 shows the set up of the scenario.

As result, the Figures 5 and 6 illustrate how the force mining has influenced the the firsts periods of the optimization, which mined more material due to its profitability.

Figure 7 disclose the constraint validation surface, used as restrict mining.

Figure 8 shows the final result regarding the force and restrict mining features, which respected the surface constraints and demonstrates the capability of these features to guide results.

Figure 3: Mining sequence between force and restrict mining surfaces.
Figure 4: Scenario setup.

## 2.2. Same surface example

The following figure exemplifies how the user can take into account any pit design to make MiningMath iteratively produce more operational results, detailing a previous scenario.

In this case, the user needs to use the same surface in both fields, force and restrict mining, and during the same period of time to reach the exact shape of the designed surface.

Although the workflow on Figure 9 uses a designed pit, it is possible to use pits from previous scenarios as well, so that you can freeze good results and optimize further periods. Below are some examples of it:

• Getting the same: Achieve the same final pit of a previous scenario.

• Using the traditional approach: Define a pushback from 5 to 5 years.

Figura 9: Using a designed surface as force and restrict mining.

This powerful workflow allow a lot of flexibility so that the user can guide solutions based on insights and previous knowledge of the deposit. The concept is a pretty unique feature of MiningMath and such approach could be easily done by following the steps of creating surfaces and validating them on the footer bellow.