24-MMP-A5 Surface Mining Methods and Design · May 2014
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, 2014-May. 3 hours duration, closed book; one hand-written 8.5×11 inch reference sheet and an approved Casio or Sharp calculator permitted. Question 1 is compulsory (40 marks, all six parts 1.1–1.6); a candidate then selects THREE of Questions 2–6 (each worth 20 marks).
Reference texts: Hartman & Mutmansky (eds.), SME Mining Engineering Handbook, 3rd ed. (dragline stripping systems, truck-shovel productivity, mine cost estimation — the primary reference throughout this paper); Hustrulid, Kuchta & Martin, Open Pit Mine Planning and Design, 3rd ed. (block-model economics, floating/moving-cone algorithm, the Lerchs–Grossmann graph-theoretic pit-optimization method, annual push-back scheduling); Kennedy, B.A. (ed.), Surface Mining, 2nd ed., SME (dragline range-diagram geometry, stripping methods); Lerchs, H. & Grossmann, I.F. (1965), “Optimum Design of Open-Pit Mines,” CIM Bulletin, 58, 47–54.
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.
1.6.1 Block model development. The ore body is discretized into a regular 3-D grid of rectangular blocks (here 15 m×15 m×15 m, Question 6), sized to balance selectivity against the density of drill-hole assay data. Each block carries attached attributes — grade(s) by estimation (kriging or inverse-distance from drill-hole composites), rock/lithology code, density, geotechnical domain, recovery/dilution factors — built up from exploration drilling, geological interpretation and a chosen estimation method.
The single number that locates each block in 3-D space (and lets software address any block instantly without storing three separate coordinates) is its Block ID, a double-precision index computed from the block’s (i,j,k) grid position:
Given. A block model with Nx×Ny×Nz blocks, indexed i = 1…Nx (east), j = 1…Ny (north), k = 1…Nz (elevation).
Example. For a model Nx = 100, Ny = 80:
$$\text{ID} = i + (j-1)\,N_x + (k-1)\,N_x N_y$$Block (i,j,k) = (12, 5, 3) → ID = 12 + (5−1)×100 + (3−1)×100×80 = 12 + 400 + 16000 = \(\boxed{16{,}412}\). To invert (recover i,j,k from a stored ID = 16412): k = floor((ID−1)/(NxNy))+1 = floor(16411/8000)+1 = 3; remainder r = 16412−(k−1)NxNy = 412; j = floor((r−1)/Nx)+1 = floor(411/100)+1 = 5; i = r−(j−1)Nx = 412−400 = 12 — recovering (12,5,3) exactly. Real coordinates then follow from the model origin plus i,j,k×block size, e.g. Easting = E0 + (i−0.5)×15.
1.6.2 The two inclusion rules. Once grade, rock type, structural and recovery attributes are attached and each block’s net cash-flow value is computed (Question 6.1), a candidate ore block is included in the optimal pit if and only if: (1) the wall-slope (support) rule — the block cannot be mined unless every block required above it to maintain a stable wall at the design slope angle is also mined (Questions 6.1–6.3’s 45° cone), so an ore block that fails this support requirement is simply unreachable regardless of its own value; and (2) the closure-value (economic) rule — a block (or, more generally, the minimum group of blocks satisfying rule 1 needed to expose it) is included only if the SUM of the cash flows of the block and all the necessary supporting waste above it is non-negative; a positive-value ore block sitting under an even more negative waste cap must still be left in the ground. These two rules together are exactly what the moving-cone and Lerchs–Grossmann algorithms of Question 6 mechanize.
