24-MMP-A5 Surface Mining Methods and Design · May 2013
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
EGBC National Exam — Mining and Mineral Processing Engineering, 09-Mmp-A5 Surface Mining Methods and Design, 2013-May. 3 hours duration; one handwritten 8.5×11 in reference sheet permitted (not an open-book exam); only approved Sharp or Casio calculators allowed. Question 1 is compulsory (40 marks, parts 1.1–1.7); candidates then select FOUR of the six optional Questions 2–7 (15 marks each) to complete the paper.
Reference texts: Hartman & Mutmansky, SME Mining Engineering Handbook, 3rd ed. (dewatering, slope stability classification, dragline stripping geometry, truck dispatch, mine closure); Hustrulid, Kuchta & Martin, Open Pit Mine Planning and Design (moving-cone and Lerchs–Grossmann pit optimization, capital-cost estimating, truck-shovel match factor); Lerchs, H. & Grossmann, I.F. (1965) “Optimum Design of Open-Pit Mines,” CIM Bulletin (the graph-theoretic 2-D worked example this question is drawn from); O’Hara, T.A. (1980) “Quick Guides to the Evaluation of Orebodies,” CIM Bulletin, Feb. 1980, and Mular, A.L. & Poulin, R. (1998) CANCOST, CIM Special Volume 47 (capital-cost formulae); Bieniawski, Z.T. (1989) Engineering Rock Mass Classifications (RMR system).
Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.
1. Block model and unique block numbering. A block model discretizes the deposit into a regular 3-D array of fixed-size cubes or rectangular prisms (e.g. this exam’s 15×15×15 m blocks), each carrying an estimated grade, tonnage, rock type and, once economics are applied, a cash flow. Each block is addressed by three indices (I, J, K) along the mine’s X, Y and Z axes; a single unique block number is generated from a fixed encoding such as $N = I + (J-1)\cdot N_x + (K-1)\cdot N_x N_y$, where $N_x, N_y$ are the model’s row/column counts. The encoding is reversible – given N, K, J and I are recovered by successive integer division/modulo by $N_x N_y$ and $N_x$ – and real-world coordinates follow from the model origin and block size, $X = X_0 + (I-\tfrac12)\Delta x$ (similarly Y, Z).
2. Cost definition. Each block carries mining cost (drill, blast, load, haul – usually a single $/tonne rate, sometimes varying with bench depth or haul distance) applied to every block regardless of grade, plus processing cost (crush/grind/concentrate, $/tonne milled) applied only to blocks scheduled to the mill, plus G&A and reclamation cost allocated on a $/tonne-mined or $/tonne-milled basis as appropriate. Costs are estimated from current operating data or, at study stage, from parametric cost models (e.g. the O’Hara-type formulae used in Question 7).
3. Grade → revenue → cash flow. Revenue per tonne is $R = g \cdot \text{recovery} \cdot \text{payable factor} \cdot \text{metal price} - \text{smelter/refining and freight charges}$, where $g$ is the block grade. Block cash flow is then $CF = (R - \text{processing cost})\cdot\text{tonnage} - \text{mining cost}\cdot\text{tonnage}$ if the block is sent to the mill, or $CF = -\text{mining cost}\cdot\text{tonnage}$ if it is waste. This is exactly the process that produces the Figure 3.1.1 cash-flow matrix used in Question 3.
4. Below-cutoff material. A block whose grade would yield $R < \text{processing cost}$ (a positive grade but an uneconomic one) is, by the standard rule base, still assigned the waste mining cost only (not sent to the mill) – it is treated identically to a zero-grade block for pit-optimization purposes, since processing it would destroy value. The one exception is where a low-grade stockpile option exists (part 5).
5. Least-loss rule (2 marks). “Least loss” compares the three possible dispositions of a marginal block – mill now, stockpile for later processing, or discard as waste – and assigns the block to whichever option minimizes the net loss relative to its full potential value, not simply whichever has the highest immediate cash flow. The rule base is: compute (a) mill-now cash flow, (b) stockpile cash flow (revenue at a future, time-discounted price less rehandle cost, minus mining cost), and (c) waste cash flow ($-\text{mining cost}$); the block is routed to the option with the highest (least negative) value, with stockpiling typically winning for blocks just below the mill cutoff but above the true breakeven (waste) cutoff, since the ore value is preserved for later rather than being permanently lost underground in the pit wall.
