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24-MMP-A5 Surface Mining Methods and Design · December 2018

Question 10 of 27

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper
Paper: Surface Mining Methods and Design (09-MMP-A5), National Exam, December 2018 — 20 pages, compulsory Question 1 (40 marks, parts 1.1–1.8) plus THREE of five optional Questions 2–6 (20 marks each) normally constitute a complete paper. As a study resource, this solution answers Question 1 in full AND all five optional Questions 2–6.

Reference texts: Hustrulid, Kuchta & Martin, Open Pit Mine Planning and Design (3rd ed.) — truck-shovel match factor, dragline stripping geometry, capital cost indexes, open-pit scheduling; SME Mining Engineering Handbook (3rd ed.) — equipment costing, mine dewatering, cost-index escalation.

Question 2.2 closed-out vs. dispatched routing, Figure 2.1 (6 marks)

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.

Given. Load time (either commodity) 3 min, dump time 1 min. Own-shovel routes: Shovel1↔Crusher 12/8 min; Shovel2↔Dump 12/8 min. Cross routes: Crusher→Shovel2 4 min; Dump→Shovel1 3 min.

Given data — Figure 2.1 travel/load/dump times (min)
SegmentTime (min)
Shovel 1 → Crusher12
Crusher → Shovel 18
Shovel 2 → Waste Dump12
Waste Dump → Shovel 28
Crusher → Shovel 2 (cross)4
Waste Dump → Shovel 1 (cross)3
Load (ore or waste)3
Dump (ore or waste)1

Find. Closed-out vs. dispatched cycle times, theoretical trucks, match factors, and the resulting productivity/cost comparison.

2.2.1 — definitions. A closed-out route dedicates each truck permanently to ONE shovel–dump pair, always returning empty by the SAME leg it arrived on (Shovel1↔Crusher, Shovel2↔Dump as two separate, self-contained loops). A dispatched route lets a truck, once empty at either dump point, be sent back to WHICHEVER shovel currently needs a truck most (using the cross legs Crusher→Shovel2 and Dump→Shovel1 as well as the direct legs), pooling the whole fleet across both shovels rather than partitioning it.

Shovel 1 Shovel 2 Crusher Dump closed-out (own leg both ways)
Fig. S2.2.1a — closed-out: Shovel1–Crusher and Shovel2–Dump each a self-contained loop (own return leg).
Shovel 1 Shovel 2 Crusher Dump cross-return legs (4, 3 min)
Fig. S2.2.1b — dispatched: empty trucks cross-route (Crusher→Shovel2, Dump→Shovel1) to whichever shovel needs a truck.

Approach. Sum each configuration’s own-leg loop for the closed-out cycle time; sum the shortest available return legs for the dispatched combined loop; convert both to theoretical trucks via Nt=Tc/Tl.

  1. 2.2.2 — closed-out cycle, trucks, MF. $$T_{c,S1} = 3+12+1+8 = 24\text{ min}, \quad T_{c,S2}=3+12+1+8=24\text{ min}$$ Both circuits are identical. Theoretical trucks per circuit: $$N_t = \dfrac{24}{3} = \boxed{8 \text{ trucks each}}$$ (16 total for both shovels). Using 8 trucks on either circuit, MF=(8×3)/(1×24)=$$\boxed{MF=1.0}$$ for either circuit working independently.
  2. 2.2.3 — dispatched combined loop. Dispatch always sends an empty truck the SHORTER way home: from the Crusher, min(8 to S1, 4 to S2)=4 (→S2); from the Dump, min(3 to S1, 8 to S2)=3 (→S1). This links the two shovels into ONE shared loop: $$T_{combined} = 3+12+1+4+3+12+1+3 = 39\text{ min for 2 loading events (1 ore + 1 waste)}$$ For each shovel to see a new truck every 3 min (its own load time), the fleet needs $$N_{t,dispatched} = \dfrac{39}{3}$$ $$\boxed{N_{t,dispatched} = 13 \text{ trucks (total, both shovels)}}$$ — 3 fewer than the 16 required closed-out, for the SAME production, because every empty return now takes the shorter of the two available legs.

2.2.4 — most efficient configuration. Dispatched is more efficient: it delivers the identical shovel-limited production (2.2.5) with only 13 trucks instead of 16 — a smaller, cheaper fleet achieves the same tonnage because no truck is ever sent home the long way when a shorter route back to an equally-needy shovel exists.

2.2.5 — shift productivity. The 12-hour shift less 1.5 h meals, 1.5 h snacks (3×0.5 h) and 1.0 h start-up/shutdown leaves 8 productive hours (480 min), confirming the stated split. With enough trucks present (either configuration), each shovel is the bottleneck, loading continuously every 3 min: $$\text{loads/shovel} = \dfrac{480}{3} = \boxed{160 \text{ truckloads}}$$ so 160 loads reach the Crusher (via Shovel 1) and 160 reach the Waste Dump (via Shovel 2) — 320 total loads — under BOTH configurations, since production is shovel-limited either way. The difference is fleet size: closed-out needs 16 trucks (8+8) to sustain it, dispatched needs only 13.

ConfigurationTruckloads to crusherTruckloads to dumpTrucks required
Closed-out16016016 (8+8)
Dispatched16016013
Check — these are idealised, zero-queueing theoretical maxima (perfectly synchronised arrivals, 100% mechanical availability, no breakdowns or blast delays). A real fleet needs a modest surplus above the theoretical minimum (spares for maintenance cycling, MF buffer per 2.1.6) to sustain this rate in practice, so 13/16 trucks are lower bounds, not the recommended live fleet size.

2.2.6 — savings from dispatching. Dispatching cuts the required fleet from 16 to 13 trucks (a 3/16 ≈ 18.8% reduction) for IDENTICAL production. Illustrating with a representative large rigid-frame haul truck (≈$3.5M capital, ≈$180/operating-hour all-in incl. fuel, tyres, maintenance, operator): capital saved ≈ 3 × $3.5M = $10.5M, and operating saved ≈ 3 trucks × 2,000 operating-hr/yr × $180/h ≈ $1.08M/yr. Savings COMPONENTS: (1) capital — 3 fewer trucks purchased; (2) direct operating — 3 fewer operators, less fuel and tyre wear; (3) indirect — less congestion/queueing at both dump points, and lower maintenance-shop loading. (Figures are an illustrative example on representative unit costs, not paper-supplied data — flagged accordingly.)