Question 4 of 13: Block Models and Pit-Inclusion Rules

Question 1.4: Block Models and Pit-Inclusion Rules (6 marks, compulsory)

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.

1.4.1 – Block model development. A block model discretises the deposit and its surrounding waste rock into a regular three-dimensional array of fixed-size rectangular blocks (Question 4 uses 15×15×15 m blocks). Grade at each block is interpolated from drill-hole assay data using a geostatistical method (typically kriging), and each block is then indexed to a unique $(i,j,k)$ column/row/level position so it can be recovered as real-world $(X,Y,Z)$ coordinates and back. The single most important piece of information attached to each block, once grade is known, is its own net economic value (cash flow) – revenue if mined and processed, less mining and processing cost – because that single number is what every pit-optimization algorithm (moving cone, Lerchs–Grossmann; Question 4) actually operates on, not grade directly.

1.4.2 – The two pit-inclusion rules. After wall-slope, rock-type, structural, and recovery factors have been folded into each block's cash flow, a block is included in the “optimal” pit if and only if BOTH of the following hold: (1) taken on its own, sending the block to the plant yields a positive cash flow (revenue exceeds its own mining plus processing cost – otherwise it is reclassified as waste, Question 5.1.4); and (2) there EXISTS at least one feasible extraction sequence (a “cone” or graph arc-set respecting the maximum wall-slope angle) reaching that block whose CUMULATIVE value – the block's own value minus the cost of removing every block of overlying/surrounding waste the slope constraint forces to be mined first – is still positive. A block can individually satisfy rule (1) and still be excluded if every feasible path to it fails rule (2) (i.e. the overlying stripping cost required to reach it exceeds its own value); this is exactly the situation Question 4.2.1.3's semicircular pit example illustrates, where individual faces are uneconomic alone but the pit as a whole, mined together, passes rule (2).