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.
5.1 — Over-trucking a shovel. If twice the theoretically required number of trucks is assigned to one shovel, the shovel itself stays 100% utilized (it is already the bottleneck at the correct truck count), but the EXCESS trucks simply queue at the shovel waiting to be loaded — truck utilization collapses (each truck now spends roughly half its cycle idle in the queue instead of hauling), fuel/tyre/operator cost per tonne moved rises sharply, and congestion on the loading bench and haul road increases the accident risk, all for no gain in shovel or system tonnage — the extra trucks would be far better deployed on an under-trucked shovel elsewhere in the pit.
5.2.1 — Manufacturers’ match factor. Equipment manufacturers define match factor as the ratio of the total loading DEMAND the truck fleet presents to the total loading CAPACITY the shovel fleet supplies: $$MF = \frac{N_t \times T_l}{N_s \times T_c}$$ where $N_t$ = number of trucks, $T_l$ = loading time per truck, $N_s$ = number of shovels, $T_c$ = truck cycle time. MF = 1 means the fleets are perfectly matched (shovel and trucks both 100% utilized); MF > 1 means trucks queue (shovel-limited, as in 5.1); MF < 1 means the shovel waits on trucks. Example: with $T_l=3$ min, $T_c=24$ min, one shovel ($N_s=1$): $MF=1$ at $N_t = T_c/T_l = 8$ trucks — exactly the closed-out result of Question 5.5.1 below.
5.2.2 — Feasibility engineers’ match factor. Over the life of the pit, a feasibility engineer cannot use a single snapshot match factor, because haul distance (and hence $T_c$) grows as the pit deepens and truck/shovel availability and utilization factors are never 100%. The life-of-pit definition instead weights the ratio by scheduled availability/utilization and is evaluated year-by-year against the SCHEDULED haul profile: $$MF_{year} = \frac{N_t \, T_l \, E_t \, U_t}{N_s \, T_c(\text{year}) \, E_s \, U_s}$$ so the fleet size that is “matched” in Year 1 (short haul) is deliberately UNDER-matched by Year 10 (long haul) unless trucks are added — this is exactly the fleet-staging trade-off analysed in Question 4.5.
Given (5.3). Load 3.0 min, loaded haul 12.0 min, backup+dump 1.0 min, empty return 8.0 min.
5.4 — Closed out vs. dispatched. Closed out routing dedicates each truck permanently to ONE shovel–dump pair (ore trucks only ever cycle Shovel 1↔Crusher, waste trucks only ever cycle Shovel 2↔Waste Dump) — simple to supervise but wastes the shorter cross-routes shown in Figure 5. Dispatched routing pools the whole fleet and sends each truck, after dumping, to WHICHEVER shovel needs a truck next (using the short cross-legs Crusher→Shovel 2 and Waste Dump→Shovel 1), keeping both shovels fed with fewer total trucks.
Given (5.5). Shovel 1(ore)→Crusher 12 min, Crusher→Shovel 1 8 min; Shovel 2(waste)→Waste Dump 12 min, Waste Dump→Shovel 2 8 min; Crusher→Shovel 2 4 min; Waste Dump→Shovel 1 3 min; load at Shovel 1 3 min, dump at Crusher 1 min; load at Shovel 2 3 min, dump at Waste Dump 1 min.
| Quantity | Result |
|---|---|
| 5.3 Theoretical truck cycle time | 24.0 min |
| 5.3 Cycle/load ratio (100%-match trucks/shovel) | 8.0 |
| 5.5.1 Closed-out trucks required | 16 (8 per shovel) |
| 5.5.1 Dispatched trucks required | 13 |
| 5.5.2 More efficient configuration | Dispatched (13 < 16 trucks for the same 2-shovel output) |
| 5.5.3 Theoretical loads/8 h shift (each shovel / total) | 160 / 320 (not realistic — see below) |
5.5.2 — Most efficient configuration. Dispatched routing is more efficient: it keeps BOTH shovels at 100% utilization with only 13 trucks, versus 16 for closed-out — a 19% fleet reduction for the identical two-shovel output, because it exploits the shorter Crusher→Shovel 2 and Waste Dump→Shovel 1 legs that closed-out routing never uses.
5.5.3 — Loads per 8-hour shift. At full utilization each shovel loads one truck every $T_l=3$ min: $$\text{loads/shovel} = \frac{480\ \text{min}}{3\ \text{min}} = 160, \qquad \text{total (both shovels)} = \boxed{320\ \text{truckloads}}$$ This is a THEORETICAL ceiling, not a realistic shift total: it assumes zero queuing delay, perfectly timed dispatch, no equipment breakdowns, no shift-change/blast/weather delays and no operator variability. Real operations typically achieve 60–85% of this theoretical rate once those losses are included — i.e. roughly 190–270 combined loads in a real 8-hour shift would be a more realistic expectation for this system.
5.6 — BP, LP and DP dispatch. BP (Best Path) is a simple greedy rule: each truck, on becoming free, is sent to whichever shovel currently has the shortest queue/longest idle wait — cheap to compute, reacts instantly, but is myopic (it can leave the fleet poorly positioned a few cycles later). LP (Linear Programming) formulates dispatch as an optimization over a full shift or day — e.g. minimizing total truck-hours or maximizing tonnage subject to grade-blend and stripping-ratio constraints — and assigns trucks to routes according to the LP’s optimal flow solution; it is globally better than BP but assumes conditions (haul times, availability) stay as forecast for the whole horizon. DP (Dynamic Programming) re-solves the assignment problem at each dispatch decision point using the CURRENT state (which trucks/shovels are where, right now), effectively chaining a sequence of short-horizon optimizations; it captures more of LP’s global view than BP while adapting to real-time conditions the way BP does, at higher computational cost.
5.7.1 — Dispatch hardware. GPS/GNSS receivers on every truck and shovel for real-time position; onboard computer terminals with a driver display for routing instructions; two-way radio or cellular/WiFi mesh data links back to a central dispatch server; payload-weighing (onboard scales) on trucks to confirm load size; and a central server running the dispatch algorithm (BP/LP/DP) that ingests all this telemetry and pushes route assignments back to each truck’s display in real time.
5.7.2 — Grade control and stripping-ratio constraints. These are encoded as constraints in the dispatch optimization (LP/DP): each active shovel/face is tagged with its current block-model grade (from grade control), and the system routes ore trucks to blend faces so the crusher feed grade stays within the mill’s target band, while simultaneously enforcing the day’s planned ore:waste split (the stripping-ratio target) by capping how many trucks are sent to waste-only faces versus ore faces in a given period — effectively a blending and ratio constraint layered on top of the pure travel-time optimization.
5.7.3 — Managing shovel underutilization under LP. When strict grade-control and stripping-ratio constraints leave a shovel under-fed for part of a 24-hour cycle (e.g. its ore is only needed for blending during certain hours), the underuse is managed by RE-TASKING that shovel’s idle window — scheduling it onto a lower-priority waste face, planned maintenance, or a stockpile-rehandle task during its slack hours — so the fleet-wide 24-hour blend and stripping targets are still met overall even though any single shovel is not loaded continuously; the dispatch system effectively time-shares shovel capacity across tasks rather than leaving it idle.
