Question 1 of 7: Support Systems, Mining-Method Geotechnics, Hoisting, Ventilation, Haulage and Cost Indices

Question 1: Support Systems, Mining-Method Geotechnics, Hoisting, Ventilation, Haulage and Cost Indices (40 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.

1.1 — Roof support systems

1.1.1 Common anchor threaded roof bolt. A mechanical expansion-wedge point-anchor bolt: a conical wedge/collar assembly at the bolt tip is expanded against the borehole wall by torquing the threaded bolt against a face plate, giving an immediate, mechanically pre-tensioned point of anchorage a short distance into the hole. It is fast and cheap to install and well suited to relatively competent, evenly bedded roof where only a modest, evenly distributed support pressure is needed — the classic pattern-bolted room-and-pillar back. Its principal weakness is that the anchor's clamping tension relaxes with time, vibration and rock creep, so it is a short-to-medium term support unless supplemented or re-torqued.

1.1.2 Split set (friction) bolt. A slotted, tapered steel tube driven into a slightly under-sized borehole; the tube's outward spring force against the hole wall provides friction anchorage along its full embedded length rather than at a single point. Installation is very fast (no resin/grout cure time, no torquing), so split sets are the default for immediate, temporary support of fresh development headings in weak-to-moderate, fractured ground — ahead of shotcrete or as spot support — but their working capacity (typically 5–10 t) is modest and they are not relied upon for long-term or heavily loaded ground.

1.1.3 Cable bolt. A multi-strand (typically 7-wire) steel cable grouted along its full length (or a substantial bonded length) into a long borehole, commonly several to tens of metres. The long bond length and high tensile strength of the strand (often >20–25 t capacity per cable) let a cable bolt reinforce well beyond the zone disturbed by blasting, tying a potentially unstable block back to competent rock far from the excavation surface. Cable bolts are the standard reinforcement for large, long-term spans — stope backs, crown pillars over a mined-out void, and hanging walls in VCR or sub-level open stopes — where the reinforcement length needed is beyond the practical range of rebar or split-set bolts.

1.2 — Room and pillar: geology, geometry, rock strength

Geology. Room and pillar suits flat-lying to gently dipping (typically <15–20°), tabular, laterally continuous deposits of fairly uniform thickness — coal seams, potash and salt beds, and stratiform/stratabound base-metal or uranium orebodies are the classic settings. A well-defined, continuous immediate roof and floor of adequate competence is essential, since both stand unsupported (beyond bolting) between pillars for the life of the panel.

Geometry. Rooms and pillars are laid out on a regular grid (square, rectangular or staggered/checkerboard) sized by tributary-area rock-mechanics design: pillar width, room width and mining height together fix the extraction ratio, and the roof span between pillars/bolts must stay within what the immediate roof beam can self-support. Deposit thickness controls mining height directly (thin seams limit equipment access and ventilation cross-section; thick seams — see Question 2.2 — may need multi-lift "stope-and-pillar" variants).

Rock strength. Pillar strength (from empirical formulas such as Obert-Duvall or the size-effect-corrected uniaxial compressive strength of the pillar material) must exceed the tributary-area vertical stress transferred from the overburden at the mining depth — deeper deposits force either larger, lower-extraction-ratio pillars or a switch away from room and pillar altogether. Roof-beam competency governs the maximum unsupported span and the bolt pattern/length, and floor strength must be checked separately for punching or heave in weak floor rock, particularly under large pillar loads.

1.3 — Vertical crater retreat: geology, geometry, rock strength

Geology. VCR needs a steeply dipping (generally >50–60°), thick-to-massive, laterally well-defined orebody, because the method leaves a large, substantially open stope void during production — a flat-dipping or thin, irregular deposit does not give the vertical continuity or wall geometry the method needs.

Geometry. Large-diameter (150–250 mm) blastholes are drilled downward from a top-sill drift through the full stope height to an undercut/slot at the bottom sill; the stope is blasted upward in horizontal "crater" slices retreating from the undercut toward the top, so the void grows progressively taller as production proceeds. Stope dimensions (strike length, width, height) must be geometrically regular enough to keep this large open span stable for the full retreat.

Rock strength. Because VCR leaves a large open (or only subsequently backfilled) void, both the ore and, critically, the hanging-wall and footwall rock must be strong and self-supporting for the exposure duration — weak walls risk uncontrolled sloughing, dilution of the (typically high-value) ore, or stope collapse. VCR is therefore restricted to competent, blocky-to-massive rock masses with in-situ stress well within the rock mass strength; where wall rock is only "fair" (contrast with Question 1.2's room-and-pillar setting), a filled method such as cut-and-fill is preferred over VCR.

1.4 — Mine hoist fundamentals

1.4.1 Two most important rope properties. Breaking (ultimate) strength, which sets the static and dynamic safety factor against the maximum suspended load; and bending-fatigue life — the rope's resistance to wire breakage from repeated flexing over the drum and sheaves — since a hoisting rope is cycled thousands of times over its service life and fatigue, not a single overload, is the usual retirement driver.

1.4.2 Most important sizing factor. The static factor of safety: breaking load divided by the total suspended static load (empty/loaded conveyance + payload + full length of suspended rope weight) must meet or exceed the code-mandated minimum — commonly 7.5:1 to 8:1 for a man/material-hoisting rope under the BC Health, Safety and Reclamation Code and similar Canadian jurisdictions — and this SF requirement, not simply "enough strength," is what actually selects the rope diameter (see Question 4/Q7's worked shaft designs).

1.4.3 Drum-to-rope diameter ratio. The ratio governs the bending radius the rope experiences each cycle over the drum/sheave, and hence its fatigue life — a small drum relative to rope diameter bends the outer wires through a tighter radius of curvature, sharply shortening service life. Typical values run roughly 80:1 to 120:1 depending on rope construction (e.g. 6×19 vs 6×36 Warrington/Seale) and duty severity, with about 100:1 a common rule-of-thumb minimum for a production shaft hoist.

1.4.4 Overwind. A conveyance (cage or skip) that is hoisted past its normal, intended stopping position at the top of the shaft/headframe and continues travelling — potentially into the sheave deck or headframe structure — a serious, potentially catastrophic failure of the normal stopping/control system.

1.4.5 Three overwind-prevention methods. (i) An electrical final-limit switch/overwind detector, tied to a position-measuring device on the hoist, that trips power to the motor and applies the emergency brake once the conveyance passes its normal stop point — the primary, first line of protection. (ii) Mechanical decelerating devices at the top of travel — crash beams, or spring/hydraulic/timber buffers mounted at the headframe sheave deck — that physically arrest an over-travelling conveyance if the electrical protection fails to stop it in time. (iii) A programmable depth-indicator/hoist-controller with slow-down and stop cams enforcing a mandatory speed-versus-position profile, so the conveyance is electronically prevented from approaching the limits of travel at anything above a safe creep speed — a redundant, independent layer on top of (i) and (ii).

1.5 — Mine ventilation: air-velocity measurement and heat/humidity

1.5.1 Slow-moving air (a depleted, closed-off area). A timed smoke tube or smoke candle, released and timed over a measured length of airway, is the standard method — mechanical vane anemometers stall or read unreliably at very low velocities. A tracer-gas (e.g. SF₂) dilution/decay method is used where an even lower, near-stagnant flow must be quantified.

1.5.2 Moderate velocity (supplying a working stope). A rotating-vane anemometer, traversed across the airway cross-section on a systematic grid (the standard "traverse" method) and averaged, gives a representative mean velocity for a typical development or stope-supply airway.

1.5.3 High velocity (a large fan with closed doors). A pitot-tube/differential-pressure traverse is used — the vane anemometer's mechanical bearings and calibrated range are unsuited to fan-discharge velocities, whereas velocity-pressure measurement (via a pitot-static tube or the fan's own orifice/venturi instrumentation) is the standard, accurate method at a fan installation.

1.5.4.1 Water content of mine air. Measured with a sling (whirling) psychrometer or an electronic hygrometer, giving wet-bulb and dry-bulb temperature (hence relative humidity and the psychrometric "sigma heat" index). It matters because, at a given dry-bulb temperature, high humidity sharply reduces the body's evaporative-cooling capacity — the combination, not dry-bulb temperature alone, governs physiological heat stress, safe continuous working time, and the sizing of any mine-cooling (refrigeration) plant.

1.5.4.2 Productivity infrastructure in hot, deep mines. Bulk and/or spot air-cooling plant (chilled-water or ice-based refrigeration serving the primary air or local coolers); cooled refuge/rest stations; increased primary airflow and auxiliary ventilation to the working face; and heat-stress monitoring with rotated/shortened shift and rest-work cycles for crews in the hottest headings.

1.6 — Rock haulage methods (underground to surface)

Shaft skip hoisting. Rock is trammed/loaded to an ore pass and skip-loading pocket, then hoisted vertically in a friction- or drum-hoisted skip. Highest capacity of the four methods (roughly 5,000 to 50,000+ t/day for a large, mechanised production shaft) and the natural choice for deep, high-tonnage, long-life operations, at the cost of very high fixed capital (shaft, headframe, hoist plant — quantified in Question 7 below).

Decline (ramp) trucking. Diesel haul trucks drive a graded (typically ~1:7, ~14–15%) spiral or switchback decline from the orebody to a surface stockpile or crusher. Moderate capacity (roughly 500 to 5,000 t/day depending on fleet size and decline length), lower fixed capital than a shaft, and flexible to extend or re-route — the usual choice for moderate-depth, moderate-tonnage or shorter-life operations (see Question 6).

Belt conveyor. Ore is crushed underground (or at a shaft-bottom/decline-portal crusher station) and moved on a belt conveyor along a decline or sub-horizontal drift. High sustained capacity (roughly 2,000 to 20,000+ t/day) at low operating cost per tonne for a long, continuous haul, but needs a controlled, sized feed and a fixed alignment — well suited to a mature, high-tonnage operation with a stable mine plan.

Rail haulage. LHDs or loaders feed ore passes or muck directly into rail cars, hauled by locomotive to the shaft bottom or a portal. Lowest of the four capacities (a few hundred to a few thousand t/day) and largely superseded by trackless (LHD/truck) systems, but still used in some deep, narrow-vein or older mines where track infrastructure is already established.

1.7 — Mine cost-estimating index terms

1.7.1 Marshall & Swift Mine/Mill (M&S M/M) cost index. A published, regularly updated (historically quarterly) capital-cost escalation index — originating with the Marshall & Swift valuation service, now the Marshall Valuation Service — that tracks equipment, labour and construction cost inflation specifically for the mining/milling sector, analogous in function to the Chemical Engineering Plant Cost Index used in process industries. Built from a base-year value of 100 against a representative basket of mining equipment and construction costs, it lets an estimator escalate a known historical capital cost to a current-year estimate simply by multiplying by the ratio of current-year to base-year index — the same escalation technique applied to the O'Hara/CapCost cost formulas of Question 7 (see 7.3).

1.7.2 The "six tenths" (0.6–0.7 power / "two thirds") rule. A capacity-scaling relationship $C_2 = C_1\left(\dfrac{X_2}{X_1}\right)^{n}$ with $n \approx 0.6\text{–}0.7$ for most mining and process equipment, used to scale a known cost at one capacity/size to an estimate at a different capacity without a full re-estimate. The exponent reflects an economy-of-scale argument: 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 linear dimension), giving cost ∝ capacity^2/3 ≈ 0.67 — close to the empirically observed 0.6–0.7 range. It is reliable only within a moderate range either side of the reference capacity, and, unlike the M&S index, it says nothing about escalation through time.

1.7.3 Cost centers underlying the M&S (and similar) mining indices. A composite mining cost index is built from separately weighted, separately tracked cost centers — typically: mining equipment; milling/processing equipment; electrical equipment and distribution; instrumentation and controls; buildings, structures and general site development; and engineering, procurement and construction-management (EPCM)/indirect costs. Tracking each center separately (rather than one blended number) lets the index better reflect a project whose cost mix differs from the average — e.g. a highly mechanised, electrical-equipment-heavy mine escalates differently from a labour- and structural-steel-heavy one.