Question 1 of 6: Haulage, Hoists, Ground Support, Ventilation Measurement and Cost Estimation

Question 1: Haulage, Hoists, Ground Support, Ventilation Measurement and Cost Estimation (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 — Underground rock haulage methods

1.1.1 – 1.1.2 Four haulage methods, their capacity ranges, and typical applications. Moving broken rock from a working face to surface (or to a sub-surface crusher/loading station) is done by one, or a combination, of the four methods below.

(a) Skip hoisting in a vertical shaft. Ore is drawn by gravity or trammed to a shaft-bottom loading pocket, metered into a skip, and hoisted vertically by a drum or friction hoist to a surface headframe where it is dumped automatically at the top of travel. Typical capacity is roughly 3,000–15,000+ t/day, scaling with skip size, hoist speed and the number of compartments; it is the method of choice for deep (>600 m), long-life, high-tonnage mines — e.g. a deep Canadian Shield base-metal or gold mine — because the fixed capital in shaft and hoist is amortised over decades of production and, unlike a ramp, the hoisting cost per tonne does not keep growing as the mine gets deeper.

(b) Truck haulage on a decline ramp. Rubber-tyred underground haul trucks are loaded by an LHD and drive the ore up a spiralling decline (typical grade 1:7, about 15%) to a surface stockpile or crusher. Typical capacity is roughly 500–3,000 t/day per truck fleet at moderate depth. Trucking is favoured for shallow-to-moderate-depth, shorter-life deposits or new mines needing production quickly, because a decline can be driven and trucks can be running within months, well ahead of the years a shaft and permanent hoist would take — the trade-off being that haul cost per tonne rises steadily with depth/distance and diesel ventilation demand.

(c) Belt conveyor. Ore is crushed to a size the belt can carry, then moved continuously on a troughed conveyor along a decline or drift (practical grade limit around 15–18°). Conveyors handle very large sustained tonnages (5,000–50,000+ t/day) at low unit power and labour cost, and are the standard choice for a large, continuous producer such as a block-cave or panel-cave operation moving ore from a central crusher station to surface or to a skip-loading bin.

(d) Rail (locomotive and car) haulage. A battery or trolley-electric locomotive pulls a train of ore cars along fixed rail track in a drift or adit to the shaft loading pocket or portal. Capacity is comparatively modest, roughly 500–2,000 t/day, limited by train length, grade (rail haulage needs a near-level track, unlike a conveyor or ramp) and loading/dumping cycle time; it remains common in older, narrow-vein or smaller mines and where a level haulage drift already exists, though most new trackless mines now use trucks instead for their flexibility around variable headings.

1.2 — Mine hoist fundamentals

1.2.1 Two most important rope properties. Breaking strength (the rope must carry the static plus dynamic load with an adequate factor of safety) and flexibility/fatigue resistance (the rope must repeatedly bend around the drum and sheaves without premature wire fatigue — a function of construction, lay and wire diameter).

1.2.2 Most important sizing factor. The maximum static load the rope must carry — the sum of the skip/cage dead weight, the full payload, and the suspended weight of the rope itself at maximum depth — checked against the rope's breaking load at the required minimum static factor of safety (commonly 7.5:1 or higher under Canadian mine safety regulations); dynamic (acceleration) loads and fatigue life are then checked once a candidate diameter passes this static test.

1.2.3 Drum-to-rope diameter ratio. This ratio governs the bending fatigue life of the rope: every trip around the drum/sheave imposes a bending stress on the individual wires that is inversely proportional to the drum diameter, so a small drum relative to the rope diameter bends the wires more sharply and shortens fatigue life sharply. Typical values used in practice are on the order of 80:1 to 120:1 (many codes set a practical minimum near 100:1 for a friction hoist), balancing rope life against the cost and size of an oversized drum/headframe.

1.2.4 Overwind. Overwind is the condition where the skip or cage travels past its intended stopping point at the top of the shaft/headframe — through operator error, brake or control failure — and continues upward toward (or into) the sheave/headframe structure, risking a dropped load, rope failure or structural collision.

1.2.5 Three overwind-prevention methods. (1) An overwind limit switch tied to the rope-drum position/depth indicator that automatically cuts hoist power and applies the emergency brake once the conveyance passes a preset point short of the sheave. (2) A mechanical decking/crash-beam arrestor (catch device) at the headframe that physically stops or safely decelerates a conveyance that has already passed the electrical limit. (3) A rope-drum (depth) position indicator with programmed slow-down and stop cams (e.g. a Lilly-type controller) that automatically reduces hoist speed and then stops the conveyance at the correct position on every normal trip, so overwind requires a genuine control failure rather than routine operator judgement.

1.3 — Rock bolting mechanism and support-system comparison

1.3.1 Mechanism. A rock bolt works either by suspension — anchoring a potentially loose block or bed to a competent stratum beyond it, so the block hangs from (rather than falls under) its own weight — or by beam-building/confinement, where a pattern of bolts clamps several thin, weak bedding layers or a jointed rock mass together into a single thicker, stiffer composite "beam" or arch that can span the opening on its own increased stiffness and internal friction. Both mechanisms rely on the bolt developing a real mechanical or bonded anchor within rock that is itself capable of carrying load.

Roof bolts have no effective anchoring capacity under two related geological conditions: (i) where the rock beyond the bolt's full length is itself incompetent or closely fractured/blocky (no continuous competent stratum exists within reach to suspend from, and no confinement action can stiffen rock that has no residual cohesion to begin with); and (ii) where a major discrete structure — a fault, shear zone or through-going joint set with significant displacement potential — cuts across the bolt pattern, since slip on that structure simply shears the bolts rather than being resisted by them. Heavily weathered, swelling or water-saturated ground can likewise defeat a mechanical or grouted anchor's bond strength even where the rock looks intact.

1.3.2 Support-system comparison.

(1) Common anchor/head threaded roof bolt (mechanical, expansion-wedge anchor). A steel bolt with an expanding wedge anchor that opens at the toe of the hole when the bolt is torqued against a face plate and nut. Design/usage: quick, low-cost, immediately load-bearing on installation — standard for temporary or short-term support in weaker, jointed but not badly broken ground, e.g. routine development headings. Mechanism: pure point-anchor suspension — all load transfer happens at the toe anchor, so its capacity depends entirely on the competence of rock right at that point.

(2) Split-set friction bolt. A slotted steel tube, slightly oversized relative to the drilled hole, driven in so the tube's spring-back grips the hole wall by friction along its whole length. Design/usage: the fastest bolt to install (no torque-up, no grout cure time), widely used for immediate, temporary ground support right at the advancing face in development headings. Mechanism: distributed frictional confinement rather than a discrete anchor, giving a lower ultimate capacity than a grouted bolt and more susceptibility to corrosion loss over time, which is why it is treated as a temporary/initial support rather than the permanent system.

(3) Resin-grouted rebar (rock) bolt. A ribbed steel rebar bonded to the hole wall along its entire length by fast-set then slow-set polyester resin cartridges. Design/usage: the standard permanent/primary support bolt in production and permanent development headings once the initial temporary support is in and the heading is stable. Mechanism: full-column bonded confinement, giving both the beam-building action (clamping bedding/joints together) and, if pre-tensioned, a suspension component — the highest ultimate capacity of the four systems.

(4) Cable bolts. Multi-strand steel cable, cement- or resin-grouted along its length, installed in long holes (many metres, well beyond a rigid rebar's practical length). Design/usage: stope-back and pillar reinforcement in open-stope mining (longhole, VCR) where the span to be supported is far larger than a rebar bolt can reach, and where the cable's flexibility lets it be fed around obstacles and installed from a single access point. Mechanism: full-length bonded confinement exactly like resin rebar, but at much greater length and lower stiffness per unit length, suiting it to reinforcing a large excavated span rather than a single heading.

1.4 — Measuring air velocity, and managing heat and humidity

1.4.1 Minimal/slow-moving air (2 marks). At very low velocities a rotating-vane anemometer stalls or reads unreliably, so a smoke-tube (or smoke candle) tracer test is used instead: a measured puff of smoke is released and the time it takes to travel a measured distance along the airway is timed, giving velocity $= \text{distance}/\text{time}$ directly — a purely visual, qualitative-instrument method well suited to a slow-moving or nearly stagnant depleted area.

1.4.2 Moderate velocity (1 mark). A rotating-vane anemometer, traversed systematically across the airway's cross-section (a grid of equal-area readings, timed over a fixed interval) and averaged, is the standard instrument for the moderate velocities typical of a working stope's intake or return airway.

1.4.3 High velocity (1 mark). At a large fan installation with closed adjacent doors — high, often turbulent velocity in a confined duct — a pitot-tube differential-pressure traverse (or a hot-wire anemometer) is preferred over a vane instrument: a vane's bearing wear and mechanical inertia become inaccurate at high speed and the fan casing rarely offers the traverse access a vane instrument needs, whereas a pitot tube measures velocity pressure directly at a point and converts it to velocity via $v=\sqrt{2\Delta p/\rho}$, and can be read through a small static port.

1.4.4.1 Measuring water content, and why it matters (2 marks). Water content (humidity) is measured with a sling (whirling) psychrometer — paired wet-bulb and dry-bulb thermometers, whirled to ensure adequate airflow over the wet wick — or an electronic hygrometer, giving relative humidity directly or via a psychrometric chart. It matters critically in a hot, deep mine because the body cools itself primarily by evaporating sweat; at high relative humidity the air is already close to saturated and cannot absorb much more moisture, so evaporative cooling collapses even at a dry-bulb temperature that would otherwise feel tolerable, and the wet-bulb temperature (not the dry-bulb alone) becomes the true measure of heat-stress risk.

1.4.4.2 Infrastructure to improve productivity (2 marks). Mechanical refrigeration — surface or underground bulk air coolers chilling the primary intake air, supplemented by spot coolers at the working face — directly lowers both the dry-bulb and wet-bulb temperature of the air reaching workers, restoring evaporative cooling capacity; this is combined with increased ventilation quantity at the working face (more air exchanges carry away metabolic and machine heat faster) and administrative controls such as work-rest cycling and hydration stations keyed to a measured heat-stress index (e.g. wet-bulb globe temperature). Together these keep the working environment's effective temperature within a range where labour productivity and safety are maintained rather than degraded by heat stress.

1.5 — Capital and operating cost estimation fundamentals

1.5.1 The "six-tenths rule" (2 marks). The six-tenths rule is the empirical capital-cost scaling relation $C_2 = C_1(S_2/S_1)^{0.6}$: the capital cost of a piece of process plant or mine infrastructure scales with its capacity (throughput, size) raised to roughly the 0.6 power rather than linearly, reflecting that the cost-driving quantities (structural steel, vessel surface area, foundation size) grow more slowly than the capacity itself (an economy of scale). It is applied in underground mine costing whenever a quick capital estimate is needed for a piece of equipment or facility of a DIFFERENT size than one already priced — e.g. scaling a known hoist, crusher or ventilation-shaft cost from a reference capacity to the capacity actually required — without redoing a full engineering estimate; the exponent is a generic default and is replaced by an equipment-specific exponent (commonly quoted between about 0.5 and 0.85 depending on the item) whenever better data exists, as used for the individual cost-centre formulas in Question 2.

1.5.2 Marshall & Swift Mine/Mill index; other indices (2 marks). The Marshall & Swift Mine/Mill cost index is a published, periodically updated index tracking the average escalation of mining/milling equipment and installation costs over time, used to convert a historical cost estimate to present-day dollars via $C_{\text{now}} = C_{\text{then}}\times(\text{Index}_{\text{now}}/\text{Index}_{\text{then}})$ — exactly the escalation method applied to the O'Hara/Mular & Poulin formulas in Question 2. Other example indices used in mine/plant cost estimation include the Engineering News-Record (ENR) Construction Cost Index, the Statistics Canada Non-Residential Building Construction Price Index, the general Consumer Price Index (a poor proxy for capital equipment but sometimes used for labour escalation), and the historical USBM/Camm parametric mine capital and operating cost indices.

1.5.3 Cost centers behind the index; their importance (3 marks). The Marshall & Swift (and similar) indices are built up from several distinct cost centers tracked and escalated separately before being combined — typically: mining/process equipment (drills, LHDs, hoists, mills — the largest single capital category, most sensitive to commodity steel and manufactured-equipment price swings); installation and materials handling (erection labour, piping, conveyors — often escalates faster than equipment cost alone due to skilled-labour scarcity); buildings and structures (headframe, mill building, maintenance shops — tracks general construction cost trends more than equipment trends); and electrical and instrumentation (substations, distribution, control systems — increasingly significant as automation content rises). Their importance to viability studies is that a project's actual cost mix rarely matches the index's blended average exactly — a mine that is unusually equipment-heavy (e.g. a highly mechanised trackless operation) or unusually structure-heavy (surface infrastructure in a remote, cold climate) will see its real capital cost escalate faster or slower than a single blended index suggests, so an estimator who only escalates a single "total" figure risks materially over- or under-stating capital cost relative to one who escalates each cost centre with its own appropriate sub-index.

1.5.4 Who to ask for a same-day +/-25% estimate (1 mark). A senior mine cost estimator/estimating engineer (in-house, or from a specialist mining cost-consulting group) who maintains current parametric cost models and recent comparable-project benchmark data — using order-of-magnitude parametric formulas of exactly the O'Hara/Mular&Poulin/Camm type applied in Question 2, capacity and depth alone are enough to generate an AACE Class 4/5, +/-25–30% estimate within a day, without waiting for the detailed engineering that a tighter estimate would require.