Mining Goes Digital – Mueller et al. (Eds)
© 2019 Taylor & Francis Group, London, ISBN 978-0-367-33604-2
272
A procedure to generate optimized ramp designs using
mathematical programming
N. Espejo, P. Nancel-Penard & N. Morales
DELPHOS Mine Planning Laboratory, Advanced Mining Technology Center (AMTC)
and Department of Mining Engineering, University of Chile, Santiago, Chile
ABSTRACT: Open-pit mine planners have long relied on optimization models for
estimating pushbacks without ramps at the block level. Subsequently, they generate an
operational design which includes ramps that are required to access the different parts of the
mine. This design depends on the time available and the experience of the planner.
In this paper, we present a procedure that (i) uses mathematical optimization to find a
modified pushback, which contains the ramp location at the block level, minimizing the
impact on the value of the original pushback, and (ii) produces a designed pushback
integrating the operational ramp design at the actual pit profile from the modified pushback.
We apply this procedure on several block models and compare to the original pushback,
the modified pushback, and the designed pushback. The results show that the designed
pushback are consistently close to the original pushback in terms of value and tonnage.
1 INTRODUCTION
Open pit mine planning is a decision-making process that leads to a realistic and actionable
plan to profitably extract mineral resources. Planning can be carried out for a wide range of
periods from the very short (next shift) to the very long (life of mine) (Whittle, 2011).
The starting point of the mine planning process is a block model in which the ore body is
divided into regular blocks; each block with individual attributes, such as, ore grades, recoveries, and tonnages. The block model is economically valued and the profit is assigned to each
block (Bley et al., 2010). This block model together with the geotechnical constraints and the
long term economic parameters (costs and commodity prices) is the basic inputs for open pit
strategic mine planning.
This models allows to compute, for example, the ultimate pit (or final pit), which is a
set of blocks in the block model that contains the total maximum profit while satisfying
the operational requirement (Cacetta & Hill, 2003). Within the ultimate pit, the deposit is
divided into nested pits: from the smallest pit with the highest value in terms of profit to the
largest pit with the lowest profit value (Dagdelen, 2001) for the purpose of establishing a
mining sequence. Nested pits are generated by varying the price of the metals being extracted
(Hustrulid et al., 2013b).
However, while the ultimate (and nested pits) are widely used for computation of plans,
there are no blocks in real mines. Indeed, these computations are used as a guide in later
stages to design actual mine. That is, they are only an approximation of the actual volumes of
the pit. Indeed, after obtaining the ultimate pit and nested pits, mine designs which represent
real profiles (for example with access ramps) are carried out.
On the one hand, the process for computing the ultimate pit and nested pit rely on
optimization techniques that guarantee that an optimal solution will be obtained. On the other
hand, the open pit operational design stage is carried out using specialized design software,
which are tools to aid the user to make designs faster but they do not ensure the profit optimization. Thus, this stage is mostly a manual process in which the optimality depends on the user.
© 2019 Taylor & Francis Group, London, ISBN 978-0-367-33604-2
272
A procedure to generate optimized ramp designs using
mathematical programming
N. Espejo, P. Nancel-Penard & N. Morales
DELPHOS Mine Planning Laboratory, Advanced Mining Technology Center (AMTC)
and Department of Mining Engineering, University of Chile, Santiago, Chile
ABSTRACT: Open-pit mine planners have long relied on optimization models for
estimating pushbacks without ramps at the block level. Subsequently, they generate an
operational design which includes ramps that are required to access the different parts of the
mine. This design depends on the time available and the experience of the planner.
In this paper, we present a procedure that (i) uses mathematical optimization to find a
modified pushback, which contains the ramp location at the block level, minimizing the
impact on the value of the original pushback, and (ii) produces a designed pushback
integrating the operational ramp design at the actual pit profile from the modified pushback.
We apply this procedure on several block models and compare to the original pushback,
the modified pushback, and the designed pushback. The results show that the designed
pushback are consistently close to the original pushback in terms of value and tonnage.
1 INTRODUCTION
Open pit mine planning is a decision-making process that leads to a realistic and actionable
plan to profitably extract mineral resources. Planning can be carried out for a wide range of
periods from the very short (next shift) to the very long (life of mine) (Whittle, 2011).
The starting point of the mine planning process is a block model in which the ore body is
divided into regular blocks; each block with individual attributes, such as, ore grades, recoveries, and tonnages. The block model is economically valued and the profit is assigned to each
block (Bley et al., 2010). This block model together with the geotechnical constraints and the
long term economic parameters (costs and commodity prices) is the basic inputs for open pit
strategic mine planning.
This models allows to compute, for example, the ultimate pit (or final pit), which is a
set of blocks in the block model that contains the total maximum profit while satisfying
the operational requirement (Cacetta & Hill, 2003). Within the ultimate pit, the deposit is
divided into nested pits: from the smallest pit with the highest value in terms of profit to the
largest pit with the lowest profit value (Dagdelen, 2001) for the purpose of establishing a
mining sequence. Nested pits are generated by varying the price of the metals being extracted
(Hustrulid et al., 2013b).
However, while the ultimate (and nested pits) are widely used for computation of plans,
there are no blocks in real mines. Indeed, these computations are used as a guide in later
stages to design actual mine. That is, they are only an approximation of the actual volumes of
the pit. Indeed, after obtaining the ultimate pit and nested pits, mine designs which represent
real profiles (for example with access ramps) are carried out.
On the one hand, the process for computing the ultimate pit and nested pit rely on
optimization techniques that guarantee that an optimal solution will be obtained. On the other
hand, the open pit operational design stage is carried out using specialized design software,
which are tools to aid the user to make designs faster but they do not ensure the profit optimization. Thus, this stage is mostly a manual process in which the optimality depends on the user.