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Vertical Rate

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The vertical rate of advance (VR) or sinking rate is also considered within the objective function on MiningMath, which means that it will be used to deliver the best result considering constraints hierarchyeven though it has a low priority. This parameter is defined as the vertical distance mined on each period, which depends on the pit depth and equipment available.

It is important to understand that this is also a 3-dimensional non-linear model, which means that it is a complex parameter within the optimization. The VR works as an upper bound to avoid operationally unfeasible solutions. Therefore, testing different values is a great strategy to identify opportunities that could bring the best mining sequence and NPV.

The Mining Width (MW) is an important parameter when defining the Vertical Rate. The MW and VR, together, define volumes of material for each mining period. A reduced MW might create additional challenges for the algorithm to comply with the VR. Therefore, it is important to play with different values, especially when VR is not being fully respected. Figure 1 illustrates a McLaughlin profile where the vertical rate of advance can be observed. Sub-vertical advances are also contemplated by this constraint.

Video 1: Vertical Rate: Definition, Hierarchy of Constraints & Complexity

Figure 1: Bottom width, Mining width and vertical rate of advance.

The vertical rate of advance is one of the first constraints to be relaxed within MiningMath’s Hierarchy of Constraints (read more). To ensure VR is at least closer to what you need, relax low-priority constraints manually. This way you will lead the algorithm to a more flexible scenario and a broader solution space, which may help it to find a feasible solution for the new set of constraints.

Besides, if the user aims to force a maximum vertical rate for a given period, it can be created a flat surface constraint regarding the achievable depth and input it as a Restrict Mining. Beyond that is important to notice that even the goal of achieving “process full” could result in a non-feasible solution while the VR is still respected, therefore, this feature is very sensitive to any other parameter.

Video 1: Vertical rates controlled by surface constraints


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