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Draw Control in Block Caving Using Mixed Integer Linear Programming

Draw management is a critical part of the successful recovery of mineral reserves by cave mining. This thesis presents a draw control model that indirectly increases resource value by controlling production based on geotechnical constraints. The mixed integer linear programming (MILP) model is formulated as a goal programming model that includes seven general constraint types. These constraints model the mining system and drive the operation towards the dual strategic targets of total monthly production tonnage and cave shape. This approach increases value by ensuring that reserves are not lost due to poor draw practice. The model also allows any number of processing plants to feed from multiple sources (caves, stockpiles, and dumps). The ability to blend material allows the model to be included in strategic level studies that target corporate objectives while emphasising production control within each cave. There are three main production control constraints in the MILP. The first of these, the draw maturity rules, is designed to balance drawpoint production with cave propagation rates. The maturity rules are modelled using disjunctive constraints. The constraint regulates production based on drawpoint depletion. Drawpoint production increases from 100 mm/d to 404 mm/d once the drawpoint reaches 6.5% depletion. Draw can continue at this maximum rate until drawpoint ramp-down begins as 93.5% depletion. The maximum draw rate decreases to 100 mm/d at drawpoint closure in the three maturity rule systems included in the thesis. The maturity rule constraints combine with the minimum draw rate constraint to limit production based on the difference between the actual and ideal drawpoint depletion. Drawpoints which lag behind their ideal depletion are restricted by the maturity rules while those that exceeded the ideal depletion were forced to mine at their minimum rate to ensure that cave porosity was maintained. The third production control constraint, relative draw rate (RDR), prohibits isolated draw by ensuring that extraction is uniform across the cave. It does this by controlling the relative draw difference between adjacent drawpoints. It is apparent in this thesis that production from a drawpoint can have an indirect effect on remote drawpoints because the relative draw rate constraints pass from one neighbour to the next within the cave. Tightening the RDR constraint increases production variation during cave ramp-up. This variation occurs because the maturity rules dictate that new drawpoints must produce at a lower draw rate than mature drawpoints. As a result, newly opened drawpoints limit production from the mature drawpoints within their region of the cave (not just their immediate neighbours). The MILP is also used to quantify production changes caused by varying geotechnical constraints, limiting haulage capacity, and reversing mining direction. It has been shown that tightening the RDR constraint decreases total cave production. The ramp-up duration also increased by eighteen months compared to the control RDR scenario. Tighter relative draw also made it difficult to maintain cave shape during ramp-up. However, once ramp-up was complete, the tighter control produced a better depletion surface. The trial with limited haulage capacity identified bottlenecks in the materials handling system. The main bottlenecks occur in the production drives with the greatest tonnage associated with their drawpoints. There also appears to be an average haulage capacity threshold for the extraction drives of 2000 tonnes per drawpoint. Only one drive with a capacity below this threshold achieves its target production in each period. Reversing the cave advance to initiate in the South-East shows the greatest potential for achieving total production and cave shape targets. The greater number of drawpoints available early in the schedule provides more production capacity. This ability to distribute production over a greater number of drawpoints reduces the total production lag during ramp-up. In addition to its role in feasibility studies, the MILP is well suited for use as a production guidance tool. It has been shown in three case studies that the model can be used to evaluate production performance and to establish long term production targets. The first of the studies shows the analysis of historical production data by comparison to the MILP optimised schedule. The second shows that the model produces an optimised production plan irrespective of the current cave state. The final case study emulates the draw control cycle used by the Premier Diamond Mine. The series of optimised production schedules mirror that of the life-of-mine schedule generated at the start of the iterative process. The results illustrate how the MILP can be used by a draw control engineer to analyse production data and to develop long term production targets both before and after a cave is brought into full production.