Mining Goes Digital – Mueller et al. (Eds)
© 2019 Taylor & Francis Group, London, ISBN 978-0-367-33604-2
328
A spatial clustering algorithm for orebody classification
and boundary setting
S. Li, Y.A. Sari & M. Kumral
Department of Mining and Materials Engineering, McGill University, Montreal, QC, Canada
ABSTRACT: Planning of processing capacity and production rates are challenging tasks
in mine planning, largely due to the accessibility to the orebody as well as the heterogeneity
of ore quantity and grades. In this research, a new approach is proposed to optimize the
processing streams and their capacities while considering the block destinations. Destination
policies are determined via classification and boundary setting of the orebody. The main
objective of this optimization is to design mineral plants such that the deviations from the
target grade will be minimized as well as maintaining the balance between the mine production and process capacity. The high initial costs of plant installation are also considered. As
the grade distribution within an orebody is largely heterogenous, the optimization is achieved
through using spatial clustering techniques to examine the grade distribution throughout the
orebody and comparing target grades and mineral processing costs of each possible processing plant. Two similar case studies are presented with possible processing plants to be built
along with their costs. The ideal combination of plants is selected while simultaneously determining the plant capacities and block destinations.
1 INTRODUCTION
Block classification is one of the aspects of mine design that has direct impact on the profitability of the operation. Many critical reviews on grade control techniques based on estimation and simulation have been put forward (Verly, 2005, M. Glacken, 1997, Srivastava, 1987,
Isaaks, 1990). However, one important factor that is often ignored in open pit mine planning
is the impact on the performance processing facilities while having inputs with significant
fluctuations in grades. Maintaining a consistent input for processing facilities is imperative
as deviations from the target grades of a processing stream lead to unintended losses in
recovery, which can be modelled via the Taguchi loss function (Kumral, 2015), a quadratic
function that penalizes deviation from a certain target (Taguchi, 1986). It has been proposed
that every processing stream maintains a target grade where blocks with exactly the same
grade receives no loss from processing, but those with grades different from the target get
penalized based on their deviations. Hence minimizing deviations from target grades would
lead to reduced loss in recovery and, in turn, increased value of profits from the operation.
A more consistent input for processing will also lead to a more uniform product, which tends
to be more desirable. Consequently, a spatial clustering technique was put forward to group
together the blocks that are spatially adjacent to each other with similar grade attributes in
order to form contiguous clusters, which correspond to different processing streams. Clustering algorithms such as k-means could be used to minimize with-in cluster dissimilarities,
target grades of each processing stream could then be set to the grade values of each cluster
centroid. Capacities of processing streams could be found by counting the number of data
points in each cluster. Performance of this technique will be evaluated with the overall profitability of the operation, while taking into account the high costs of constructing additional
processing facilities, so that new processing streams are built if and only if the cost more
than balances out for the losses in recovery due to deviation from target grades. Inclusion
© 2019 Taylor & Francis Group, London, ISBN 978-0-367-33604-2
328
A spatial clustering algorithm for orebody classification
and boundary setting
S. Li, Y.A. Sari & M. Kumral
Department of Mining and Materials Engineering, McGill University, Montreal, QC, Canada
ABSTRACT: Planning of processing capacity and production rates are challenging tasks
in mine planning, largely due to the accessibility to the orebody as well as the heterogeneity
of ore quantity and grades. In this research, a new approach is proposed to optimize the
processing streams and their capacities while considering the block destinations. Destination
policies are determined via classification and boundary setting of the orebody. The main
objective of this optimization is to design mineral plants such that the deviations from the
target grade will be minimized as well as maintaining the balance between the mine production and process capacity. The high initial costs of plant installation are also considered. As
the grade distribution within an orebody is largely heterogenous, the optimization is achieved
through using spatial clustering techniques to examine the grade distribution throughout the
orebody and comparing target grades and mineral processing costs of each possible processing plant. Two similar case studies are presented with possible processing plants to be built
along with their costs. The ideal combination of plants is selected while simultaneously determining the plant capacities and block destinations.
1 INTRODUCTION
Block classification is one of the aspects of mine design that has direct impact on the profitability of the operation. Many critical reviews on grade control techniques based on estimation and simulation have been put forward (Verly, 2005, M. Glacken, 1997, Srivastava, 1987,
Isaaks, 1990). However, one important factor that is often ignored in open pit mine planning
is the impact on the performance processing facilities while having inputs with significant
fluctuations in grades. Maintaining a consistent input for processing facilities is imperative
as deviations from the target grades of a processing stream lead to unintended losses in
recovery, which can be modelled via the Taguchi loss function (Kumral, 2015), a quadratic
function that penalizes deviation from a certain target (Taguchi, 1986). It has been proposed
that every processing stream maintains a target grade where blocks with exactly the same
grade receives no loss from processing, but those with grades different from the target get
penalized based on their deviations. Hence minimizing deviations from target grades would
lead to reduced loss in recovery and, in turn, increased value of profits from the operation.
A more consistent input for processing will also lead to a more uniform product, which tends
to be more desirable. Consequently, a spatial clustering technique was put forward to group
together the blocks that are spatially adjacent to each other with similar grade attributes in
order to form contiguous clusters, which correspond to different processing streams. Clustering algorithms such as k-means could be used to minimize with-in cluster dissimilarities,
target grades of each processing stream could then be set to the grade values of each cluster
centroid. Capacities of processing streams could be found by counting the number of data
points in each cluster. Performance of this technique will be evaluated with the overall profitability of the operation, while taking into account the high costs of constructing additional
processing facilities, so that new processing streams are built if and only if the cost more
than balances out for the losses in recovery due to deviation from target grades. Inclusion