273
It follows that the quality of the resulting solution depends on the skills, information and
time available for the design phase. Even if there exist some criteria to check the quality (for
example, measuring the difference in tonnage and value of the optimal pit shell versus the
operational pit design), there is no guarantee that the results would be optimal. In addition,
the process itself is very slow and time consuming, making it to analyze the robustness of the
obtained design.
Unfortunately, ramps are one of the most important aspects of mine planning and they
should be included early in the mine planning process since they do have a significant effect
on the reserves (Hustrulid et al., 2013a), because they force the addition of waste and/or
reducing the amount of ore from the pit shells.
In this paper, we build on previous work to present a methodology that uses a mathematical model and postprocessing in order to generate a pit design which is as close as possible to
the results of the optimization process, but complies with actual design considerations. The
mathematical model has been already introduced (see Morales et al. 2017 and Nancel-Penard
2019) starts with the optimized pit (at the block level or support) and generates another profile (also at the block support) with enough space for ramps and so that the impact in value
is minimized. The postprocessing, which is the emphasis of this paper, then takes this protodesign of the phase and generates a design of the pit and ramp.
1.1 Review of current practices and related literature in mine designs
At the mine design stage that consists of converting volumes defined at block level into operational ones, it is necessary to smooth the final pit contour and pushbacks. Mine designs must
incorporate all the geometrical components of a slope, which include hauling ramps, where
trucks can access each of the phases to transport ore and waste to the final destinations.
Generally, ramps’ locations are constructed based on the criteria of the mine planner in
charge of the operational mine designs of an open pit. One of the issues faced by the mine
planner, which is little written about in the mining literature, is gaining initial access to the
ore body (Hustrulid et al., 2013a). Some aspects, which the mine planner must consider when
realizing operational designs, are:
• Minimum costs on a net present value basis for the transport of ore and waste throughout
the life of mine. The preference is to use of long-life haul roads rather than short-life roads
as this reduces overall road construction costs and operating costs (Atkinson, 1992).
• Roads exits from the pit wall. This is dependent upon the crusher location and the dump
points (Hustrulid et al., 2013a).
• Optimum number of access points to the pit. More access points mean more flexibility but
the added cost could be high (Hustrulid et al., 2013a).
• Optimum number of switchbacks. It is desirable to avoid the use of switchbacks in a pit
because they tend to slow traffic, cause greater tire wear and various road maintenance
problems (Hustrulid et al., 2013a).
• Minimum traffic congestion (Atkinson, 1992).
• Avoidance of areas where slope stability problems could occur (Atkinson, 1992).
Therefore, the planner must deal with many criteria and considerations to generate a
design, which means that the current practice does not necessarily maximizes NPV and minimizes operational costs in pit designs.
2 DESCRIPTION OF THE MODEL AND POSTPROCESSING ALGORITHM
In this section we specify the problem to be solved and describe the mathematical model and
postprocessing algorithm.
Figure 1 depicts the whole process. As a first stage, we start with a pushback at the block
support (for example the ultimate pit or any nested pit). This pit used as an input for an
optimization model that looks for a pre-design pushback (also at the block support) so that:
It follows that the quality of the resulting solution depends on the skills, information and
time available for the design phase. Even if there exist some criteria to check the quality (for
example, measuring the difference in tonnage and value of the optimal pit shell versus the
operational pit design), there is no guarantee that the results would be optimal. In addition,
the process itself is very slow and time consuming, making it to analyze the robustness of the
obtained design.
Unfortunately, ramps are one of the most important aspects of mine planning and they
should be included early in the mine planning process since they do have a significant effect
on the reserves (Hustrulid et al., 2013a), because they force the addition of waste and/or
reducing the amount of ore from the pit shells.
In this paper, we build on previous work to present a methodology that uses a mathematical model and postprocessing in order to generate a pit design which is as close as possible to
the results of the optimization process, but complies with actual design considerations. The
mathematical model has been already introduced (see Morales et al. 2017 and Nancel-Penard
2019) starts with the optimized pit (at the block level or support) and generates another profile (also at the block support) with enough space for ramps and so that the impact in value
is minimized. The postprocessing, which is the emphasis of this paper, then takes this protodesign of the phase and generates a design of the pit and ramp.
1.1 Review of current practices and related literature in mine designs
At the mine design stage that consists of converting volumes defined at block level into operational ones, it is necessary to smooth the final pit contour and pushbacks. Mine designs must
incorporate all the geometrical components of a slope, which include hauling ramps, where
trucks can access each of the phases to transport ore and waste to the final destinations.
Generally, ramps’ locations are constructed based on the criteria of the mine planner in
charge of the operational mine designs of an open pit. One of the issues faced by the mine
planner, which is little written about in the mining literature, is gaining initial access to the
ore body (Hustrulid et al., 2013a). Some aspects, which the mine planner must consider when
realizing operational designs, are:
• Minimum costs on a net present value basis for the transport of ore and waste throughout
the life of mine. The preference is to use of long-life haul roads rather than short-life roads
as this reduces overall road construction costs and operating costs (Atkinson, 1992).
• Roads exits from the pit wall. This is dependent upon the crusher location and the dump
points (Hustrulid et al., 2013a).
• Optimum number of access points to the pit. More access points mean more flexibility but
the added cost could be high (Hustrulid et al., 2013a).
• Optimum number of switchbacks. It is desirable to avoid the use of switchbacks in a pit
because they tend to slow traffic, cause greater tire wear and various road maintenance
problems (Hustrulid et al., 2013a).
• Minimum traffic congestion (Atkinson, 1992).
• Avoidance of areas where slope stability problems could occur (Atkinson, 1992).
Therefore, the planner must deal with many criteria and considerations to generate a
design, which means that the current practice does not necessarily maximizes NPV and minimizes operational costs in pit designs.
2 DESCRIPTION OF THE MODEL AND POSTPROCESSING ALGORITHM
In this section we specify the problem to be solved and describe the mathematical model and
postprocessing algorithm.
Figure 1 depicts the whole process. As a first stage, we start with a pushback at the block
support (for example the ultimate pit or any nested pit). This pit used as an input for an
optimization model that looks for a pre-design pushback (also at the block support) so that: