Question 1 of 7: Ventilation, Mine Planning, Cost Indices, Hoisting and Backfill Fundamentals

Question 1: Ventilation, Mine Planning, Cost Indices, Hoisting and Backfill Fundamentals (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 — Mine ventilation circuits

1.1.1 Total, static, velocity and potential head. Total head H_t is the sum of static head H_s and velocity head H_v: $H_t = H_s + H_v$. Static head is the pressure energy available to overcome friction and shock losses along the airway — the useful, dissipated component. Velocity head is the kinetic energy of the moving air column, $H_v = \rho V^2/2$, and is largely unrecoverable once the air is discharged to atmosphere at the exhaust portal. Potential head accounts for elevation and air-density (temperature/humidity) differences between the two survey stations — in a deep or warm mine this manifests as natural ventilation pressure (NVP), which either assists or opposes the fan depending on season and shaft configuration. Between any two survey points, the fan's total head input equals the sum of the static (frictional) losses, any change in velocity head, and the potential-head term, so a ventilation survey balances $H_{t1} = H_{t2} + \Delta H_{friction} \pm H_{potential}$.

1.1.2 Atkinson equation components. The Atkinson equation, $H = RQ^2$, gives the frictional head loss of an airway, where the resistance $R = \dfrac{k P L}{A^3}$. The friction factor k characterises the roughness/rubbing-surface behaviour of the airway lining (a property of the rock or support surface, essentially an aerodynamic drag coefficient); P is the rubbing-surface perimeter of the airway; L is the airway length; and A is the cross-sectional area, which enters as $A^3$ and therefore dominates the resistance — halving an airway's area increases its resistance eightfold. Q is the air quantity, and the loss is proportional to $Q^2$ because turbulent-flow head loss scales with the square of velocity.

1.1.3 Kirchhoff's laws in ventilation networks. Kirchhoff's first (nodal/continuity) law states that at any junction the air entering must equal the air leaving — used to solve the quantity split between parallel airways, since parallel branches share the same head loss but divide the total quantity in inverse proportion to the square root of their resistance ($Q_i \propto 1/\sqrt{R_i}$). Kirchhoff's second (loop/mesh) law states that around any closed circuit the algebraic sum of head losses (and any fan heads or NVP within the loop) is zero — used to balance a branched series–parallel network. Modern mine-ventilation network solvers (VnetPC, Ventsim, ClimSim) apply both laws simultaneously through an iterative Hardy-Cross-type balancing routine to converge on the quantity and pressure distribution across the whole circuit.

1.2 — Mining-method selection for a steep, high-grade vein

Given.

At 70° dip the vein is steeply dipping (essentially past the ≈50–55° angle of repose of broken rock), which favours gravity-assisted ore flow to drawpoints and rules out the flatter room-and-pillar/sub-level caving family. A 4 m width is workable by mechanised trackless equipment without excessive dilution from a full-face blast, but it is narrow enough that a single, moderately sized stope panel spans the whole vein width. The decisive constraint is "fair" wall-rock quality: fair ground can stand a moderate exposed span for the days-to-weeks needed to blast and muck one lift, but it cannot be relied upon to stand a large, permanently open stope void — so a bulk open-stoping method (sub-level or longhole open stoping left unfilled) is not appropriate here, since it would risk uncontrolled wall sloughing and dilution of a high-grade ore. Two methods should be shortlisted: mechanised overhand cut-and-fill, which fills each lift as soon as it is mucked and so never leaves more than one lift's worth of span open — the natural choice when grade control/selectivity matters as much as ground support, and the moderate 4 m width suits a single-heading cut-and-fill drift; and longhole (sub-level) stoping with cemented rockfill immediately following each stope, which gives higher productivity than cut-and-fill at the cost of slightly coarser selectivity. Given the vein is described as continuous and high-grade (favouring maximum recovery/minimum dilution over raw tonnage rate) and the walls only "fair" (needing prompt, not delayed, support), overhand cut-and-fill is recommended as the primary method, with longhole-and-fill retained as the higher-productivity alternative if development drilling later confirms the walls are more competent than the fair rating suggests.

1.3 — Four narrow-vein underground mining methods

1.3.1 Sub-level stoping (open stoping). A series of horizontal sub-level drifts is developed through the orebody, from which long, near-vertical blastholes (rings or parallel fans) are drilled down into a large open stope void; the ore is blasted in slices and gravity-flows to drawpoints on the haulage level below, with the stope left substantially unsupported (open) for the life of the panel. It requires strong ore and wall rock, since the span stays open for an extended period, but gives high productivity and low unit cost with minimal development per tonne.

1.3.2 Longitudinal longhole retreat. The transverse-stoping concept is turned 90° and applied along the strike of a narrow (typically <4 m), steeply dipping vein rather than across it: a single elongated stope is mined in longhole slices retreating along the vein's length between two sub-levels, suited to widths too narrow for cross-strike equipment access.

1.3.3 True Avoca mining. A hybrid of open stoping and cut-and-fill developed at the Avoca mines: ore is blasted along the retreating longitudinal face and drawn while the void behind the retreat is progressively backfilled, so that production (blasting/mucking) and filling proceed concurrently in adjacent panels — the fill supports the walls once a panel is exhausted while another panel is still producing, sustaining continuous mill feed from a set of staggered panels.

1.3.4 Eureka mining method. A further narrow-vein variant of the Avoca family, distinguished by a tighter, more frequent fill cycle — each short slice is mucked and backfilled (rock or hydraulic fill) essentially immediately, rather than allowing an extended open span — minimising dilution and providing a continuous working platform in ground too weak for the longer open spans tolerated by true Avoca.

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 (originating with the Marshall & Swift valuation service, now Marshall Valuation Service) that tracks equipment and construction cost inflation for the mining/milling sector specifically, analogous in function to the Chemical Engineering Plant Cost Index used in process industries. It is developed from a base-year value of 100 and updated on a regular (historically quarterly/annual) cycle by tracking a representative basket of mining equipment, labour and material costs; an estimator escalates an old, known-year capital cost to the current year by multiplying by the ratio of current-year to base-year index — exactly the escalation technique used in Question 4.3 below with the Camm (1991) capital and operating indices.

1.4.2 The "six tenths" (0.6/0.7 power) rule. A capacity-scaling cost 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 an estimate at a different capacity without a full re-estimate. The exponent reflects economies of scale: for a roughly cube-shaped vessel or structure, surface area (and hence fabrication cost) scales with the square of a linear dimension while capacity (volume/throughput) scales with the cube, giving cost ∝ capacity^2/3≈0.67 — close to the empirical 0.6–0.7 range observed across mining equipment classes. The rule is only reliable within a moderate range either side of the reference capacity and, unlike the M&S index, says nothing about escalation through time.

1.4.3 Cost centers underlying mine cost indices. The M&S-type mining indices (and the Camm parametric models used in Question 4) are built up from standard cost centers: Labour, Equipment, Steel, Lumber, Fuel, Lubricants, Explosives, Tires, Construction materials, and Electricity — each tracked and escalated separately before being summed to a project total, which is exactly the component breakdown Table 4.1 and Table 4.2 present in Question 4.

1.5 — Mine hoisting rope types

Round-strand (regular-lay) wire rope. The conventional construction — helically laid round wires formed into strands around a core. It is the most flexible of the three types for a given breaking strength, tolerating smaller sheave and drum diameters, and is preferred for guide ropes, sinking/kibble hoisting, and smaller or temporary shaft hoists where flexibility and low first cost matter more than maximum fatigue life.

Locked-coil rope. Built with one or more outer layers of interlocking shaped (Z-profile) wires around an inner round-wire core, giving a smooth, solid, low-stretch outer surface that seals the rope against internal corrosion and resists spin/rotation under load. It has the highest strength-to-diameter ratio and the best fatigue life of the three, at the cost of requiring a larger minimum sheave/drum diameter (hence the drum/rope diameter ratio of 108 specified in Question 6). It is the standard choice for main production shaft-hoisting ropes on deep, high-duty, permanent installations — precisely the locked-coil rope specified for the 425 m shaft in Question 6.

Flattened-strand (or triangular-strand) rope. A compromise construction using pre-formed, non-round strand wires that pack more metal into a given diameter and resist crushing/wear better than round-strand rope, while remaining considerably more flexible than locked coil. It is chosen where a rope must bend over smaller sheaves more often than a main hoist rope (multi-rope Blair/Koepe head-sheave arrangements, or duty guide ropes) but still needs better wear life than plain round-strand rope provides.

1.6 — Headframe design

1.6.1 Critical design parameter — fleet angle. The controlling parameter is the fleet angle: the angle, in plan, between the rope's actual path as it winds across the width of the drum and the true vertical line through the head sheave. As the rope layer travels from one end of the drum to the other, the fleet angle grows; if it exceeds an allowable limit (conventionally about 1.5°, up to roughly 2° for grooved drums), the rope rubs against adjacent wraps and the sheave-groove flange, accelerating wear and risking the rope jumping its groove. Because the fleet angle shrinks as the sheave is raised further above the drum, this single criterion — not headroom for its own sake — is what sets the minimum required height of the headframe above the collar for a given drum width and hoisting rope centre spacing.

1.6.2 Types of headframes. Steel lattice (tower) headframes are the most common: relatively low capital cost, quick to erect, and easy to modify or extend, used at the great majority of conventional shaft installations. Reinforced-concrete headframes cost more but offer greater rigidity, durability and fire resistance, and can integrate ancillary structures (crushing station, ore bins) into the same structure — favoured for very large, high-tonnage or long-life production shafts, and for sites where seismic loading or corrosive/coastal exposure disfavour open steel. Older or short-life shafts sometimes use braced timber headframes, now largely obsolete for permanent production duty. The choice is driven by hoisting duty (rope loads and sheave elevation from the fleet-angle criterion above), shaft design life, site conditions and available capital.

1.7 — Swell factor and backfill elevation in overhand cut-and-fill

Broken (blasted) rock occupies substantially more volume than the same rock in situ, because voids form between the angular fragments; this bulking or swell factor is typically of order 1.3–1.6 (a 30–60% volume increase) depending on fragmentation and rock type. Swell matters to cut-and-fill efficiency in two distinct ways. First, it sizes the mucking and ore-pass system: the muckpile volume that must be handled through the mill-hole/ore-pass segments described in the question is 30–60% larger than the in-situ stope volume just mined, and the ore-pass, drawpoint and haulage capacity must be sized to that swollen volume, not the in-situ one. Second, and more critically for ground control, the backfill placed once mucking is complete must be brought up to an elevation that matches the in-situ (pre-swell) roof of the mined-out lift, because the fill's job is to support the true rock walls and provide a working floor at the actual mined height — not to "make up" the extra volume the swollen muck occupied while it sat in the stope. An estimator who sized the required fill volume from the swollen muck tonnage rather than the in-situ void geometry would overstate the fill required, or worse, underfill relative to the true back elevation and leave an unsupported air gap at the roof. In practice the fill is placed to slightly exceed the in-situ roof elevation (a deliberate camber/beach allowance) so that the highest points of an uneven back are still in contact with fill, since any residual air gap is where uncontrolled roof failure into the next lift originates.