Question 1 of 6: Backfill, Hoisting, Ventilation, Costs, Room-and-Pillar and VCR Mining

Question 1: Backfill, Hoisting, Ventilation, Costs, Room-and-Pillar and VCR Mining (40 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.

1.1 — Backfill systems

1.1.1 Cemented rock fill (CRF). Coarse waste rock or aggregate (broadly graded, typically minus 150–200 mm run-of-mine or crushed material) is placed in an open stope by truck, LHD or conveyor and then grouted with a cement slurry (commonly a 3–7% cement-to-fill ratio by dry weight, delivered by pipeline as a separate binder pour or a pumped paste-cement mix that percolates through the rock voids). The coarse, free-draining gradation gives a moderate unworking strength (unconfined compressive strength commonly 0.5–2 MPa at 28 days) at low binder cost, which is adequate where the fill must stand as a stable exposed face for a neighbouring stope but need not be watertight or highly stressed — making CRF the default fill for large-volume bulk stopes (sub-level open stoping, VCR).

1.1.2 Mill tailings (hydraulic) fill. Whole or classified mill tailings (fine-grained, commonly minus 150 μm, sometimes cycloned to remove the finest, most drainage-limiting fraction) are pumped underground as a low-density slurry (typically 55–65% solids by weight) and discharged into the stope through a fill raise or borehole, with a barricade and internal drainage system to bleed off excess water; a modest cement addition (2–5%) can be blended in for cemented hydraulic fill where higher strength is needed. Because it is fine, unclassified or poorly drained hydraulic fill can remain in a loose, saturated, potentially liquefiable state, so barricade design and drainage are safety-critical, not merely a placement detail.

1.1.3 Paste fill. Whole (unclassified) mill tailings are thickened to a high-density, non-segregating, non-bleeding "paste" consistency (roughly 70–85% solids by weight, essentially zero free water) and mixed with a binder (typically 3–7% Portland cement or a slag/fly-ash blend to cut cost) before being pumped — not gravity-flowed — through a pipeline into the stope. Because the whole tailings stream is used with no dewatered coarse fraction discarded, the size distribution is very fine throughout, giving the fill its low permeability and high structural competence once cured; paste fill is the standard choice for permanent structural fill, pillar-replacement fill and any exposed sill/rib pillar in selective methods such as cut-and-fill, where a competent standing face with minimal underground drainage infrastructure is required.

1.2 — Mine hoist types, creep and the Blair hoist

Single drum. One rope winds on and off a single drum to one conveyance. Advantages: simplest, cheapest, easiest to maintain; well suited to shaft sinking, exploration/development shafts and shallow, single-conveyance service. Disadvantages: no independent balancing of a second conveyance, and the full weight of rope-plus-load must be accelerated/decelerated with no counterbalance, limiting practical depth and duty cycle.

Double drum. Two drums on a common shaft, each independently clutched so its rope length can be adjusted for shaft stretch/rope wear, each serving its own skip or cage. Advantages: balanced two-conveyance service (one loaded skip ascending as the other descends empty, cutting net power), and independent clutch adjustment compensates for rope stretch over time. Disadvantages: heavier, more complex and more expensive than a single drum; drum inertia still has to be accelerated/decelerated every cycle, which limits speed/depth compared with a friction hoist.

Friction (Koepe). A single grooved friction sheave; the rope(s) pass over (not wind onto) the sheave, linking a conveyance to a counterweight or to a second conveyance, so gravity keeps the system close to balanced and the sheave itself carries little rotating mass. Advantages: much lower inertia than a drum hoist, enabling deeper shafts and higher hoisting speeds at lower installed power; commonly used with multiple parallel ropes (4–8) for very deep, high-duty production shafts. Disadvantages: depends on adequate rope–sheave friction (liner condition, wrap angle, rope tension ratio) to avoid slip, and the shallow independent-adjustment ability of a drum system is lost.

Blair multi-rope. A drum-type hoist using several small-diameter ropes wound in parallel (rather than one large rope) to a single conveyance. Advantages: spreads the static and dynamic load across multiple ropes, each individually smaller and therefore subject to less bending-fatigue stress for a given drum diameter, letting the system reach depths/capacities a single large rope could not practically achieve. Disadvantages: the parallel ropes must be kept in equal tension and length (added rigging/maintenance complexity), and losing/damaging one rope compromises the balance of the whole set.

Creep. On a friction (Koepe) hoist the rope tension differs on the two sides of the sheave (loaded side vs. counterweight/empty side); that tension difference elastically stretches the rope by a slightly different amount on each side as it passes over the sheave, producing a small relative slip between rope and sheave lining — called creep — distinct from gross slip. Creep is normal and unavoidable in a friction hoist, but must be kept small (adequate coefficient of friction, wrap angle and liner design) since excessive creep accelerates liner/rope wear, generates heat, and in the extreme can progress toward damaging slip or runaway.

1.2.2 — Applications of the Blair hoist. The Blair (multi-rope drum) hoist is used to advantage where a shaft is too deep or a duty too heavy for a single conventional rope to handle within practical drum-diameter and rope-diameter (fatigue) limits — typically deep, high-tonnage production shafts (historically common at deep Canadian Shield hard-rock mines) where a single rope large enough to carry the full static load would be too thick to wind on a reasonably sized drum without breaching the minimum drum/rope diameter fatigue ratio. Splitting the load across several smaller, parallel ropes keeps each individual rope's bending-fatigue life acceptable at a compact drum diameter, and gives a measure of redundancy (a degraded rope can sometimes be identified and managed before failure, since load-sharing makes uneven wear detectable) that a single-rope system does not offer.

1.3 — Sensible/latent heat, wet/dry bulb, Kirchhoff's Laws

1.3.1 Latent and sensible heat. Sensible heat is heat that changes the temperature of the air (and any water vapour it carries) without a phase change — it is "sensed" directly as a dry-bulb temperature rise or fall (from auto-compression, machinery, rock-wall convection, etc.). Latent heat is heat absorbed or released by a phase change of the moisture carried in the air — evaporation of water (sweat, wet rock surfaces, spray) into the airstream absorbs latent heat without raising dry-bulb temperature, while condensation of moisture out of the air releases it — and is "hidden" because it does work changing the water's phase rather than raising a thermometer reading.

1.3.2 Determining wet/dry bulb temperature and its use. Both are read with a sling (whirling) psychrometer: two thermometers side by side, one bulb left dry (reads dry-bulb temperature) and the other covered with a wetted wick and whirled through the air to promote evaporative cooling at the wick (reads wet-bulb temperature, the lowest temperature evaporative cooling can reach at the prevailing humidity). The wet-bulb depression (dry-bulb minus wet-bulb) is read against a psychrometric chart (or computed via Carrier's equation) to obtain relative humidity, humidity ratio and enthalpy; because the body's main cooling mechanism at depth is evaporative (sweating), it is the WET-bulb temperature — not dry-bulb — that governs how effectively a miner can cool, so bulk/spot air-cooling capacity and heat-stress limits (e.g. wet-bulb globe temperature indices) are set from the wet-bulb reading to keep the working environment within safe, productive limits.

1.3.3 Kirchhoff's Laws in ventilation circuits. Mine ventilation networks obey the same two conservation laws as electrical circuits. Kirchhoff's First Law (nodal/continuity law): the air quantity flowing into any junction equals the quantity flowing out, so in a SERIES circuit the same quantity Q flows through every airway in the chain, and airway resistances simply add, $R_{series}=\sum R_i$. Kirchhoff's Second Law (loop/energy law): the sum of pressure (head) losses around any closed ventilation loop is zero, so airways sharing the same two end junctions (a PARALLEL circuit) all see the SAME head loss H; because Atkinson's equation is quadratic in Q ($H=RQ^2$, not linear like Ohm's Law), parallel resistances do not add reciprocally as in an electrical circuit but combine via the square-root law $1/\sqrt{R_{eq}} = \sum 1/\sqrt{R_i}$.

1.4 — Mine cost-estimating terms

1.4.1 Marshall & Swift Mine/Mill (M&S M/M) cost index. A published capital-cost escalation index, developed by the Marshall & Swift valuation service, tracking equipment and construction cost inflation specifically for the mining/milling sector — the mining-industry analogue of the Chemical Engineering Plant Cost Index used in process industries. Built from a base-year value of 100 and updated on a regular cycle from a representative basket of mining equipment, labour and material costs, it lets an estimator escalate a known older-year capital cost to the current year simply by multiplying by the ratio of current-year to base-year index — exactly the technique used with the Table 4.3 indices in Question 4.3.

1.4.2 The "six tenths" (0.6/0.7 power) rule. A capacity-scaling relationship, $C_2 = C_1(X_2/X_1)^n$ with $n \approx 0.6\text{–}0.7$ for most mining and process equipment, used to scale a known cost at one capacity to a cost estimate at another capacity without a full re-estimate. The exponent reflects economies of scale: for a roughly cube-shaped structure or vessel, fabrication cost scales with surface area (a squared linear dimension) while capacity scales with volume (a cubed dimension), giving cost ∝ capacity^2/3 ≈ 0.67 — close to the empirically observed 0.6–0.7 range, and visible directly in the sub-unity exponents (0.591–0.946) of every category in Question 4's Table 4.2.

1.4.3 The O'Hara Method (CIM Bulletin, February 1980). A parametric, order-of-magnitude capital-cost estimating method developed by T.A. O'Hara and published in the CIM Bulletin, February 1980, expressing the major cost components of a Canadian underground mine (shaft, mine development, concentrator, supporting infrastructure) as power-law functions of mine capacity and, for shaft-related items, depth — calibrated from a historical database of actual Canadian mine costs. Like the Camm (1989) models used in Question 4, it targets rapid pre-feasibility/screening-level comparison rather than a bankable estimate, and was later extended into the Mular & Poulin CapCost system (CIM Special Volume 47, 1998).

1.5 — Room and pillar mining

Geology. Room and pillar suits flat-lying to gently dipping, tabular, stratiform deposits of fairly uniform thickness (coal, potash, trona, many sedimentary-hosted base-metal deposits) where a regular grid pattern can follow the orebody without excessive dilution from cutting into hangingwall/footwall waste. Geometry. Rooms and rectangular or square pillars are laid out on a regular grid; pillar centres and room widths follow from the required extraction ratio, and pillars are sized by tributary-area loading theory (pillar stress = overburden stress × tributary area / pillar area) checked against pillar strength (e.g. Obert–Duvall/Bieniawski formulas). Rock strength. The roof must be competent enough to bolt and span the room width without a beam-building failure, and pillar rock must carry the tributary load with an adequate factor of safety against spalling/crushing; weak pillar rock forces larger pillars (lower recovery) or partial/sequential pillar recovery later in the mine life, while weak roof rock limits the achievable room span regardless of pillar design. Broken rock is loaded by LHD (or, in mechanised coal/potash operations, continuous miners and shuttle cars/conveyors) and trammed along the rooms to ore passes or a conveyor system for hoisting to surface.

1.6 — Vertical Crater Retreat (VCR) mining

Geology. VCR suits massive, competent, steeply dipping to sub-vertical orebodies of fairly regular geometry with strong, well-defined wall rock, since it is a bulk open-stoping method with no internal support once blasted. Geometry. Large-diameter (150–250 mm) vertical blastholes are drilled from a top-sub-level drill drift down to near the undercut at the bottom sub-level, and the stope is blasted upward in successive horizontal crater slices, retreating toward the top sub-level while broken ore is drawn from drawpoints on the bottom sub-level and trammed to ore passes. Rock strength. Because the blasted void is left open — unsupported, or filled only well after blasting — for an extended period spanning the full stope height and width, both the ore and the hangingwall/footwall must be strong and self-supporting; poor-quality walls risk progressive slough, dilution and, in the worst case, uncontrolled stope collapse.