GATE MN cheat sheet

Syllabus spans: mine development and rock mechanics; underground and surface mining methods; drilling and blasting; mine ventilation and environment; mine machinery and materials handling; mine surveying; mineral processing; mine economics, safety and legislation.

Rock mechanics core relations: σ1 = σ3 + σc·(σ3/σt + 1)^0.5 is the Hoek–Brown empirical criterion; Mohr–Coulomb gives τ = c + σn·tanφ, with φ = friction angle and c = cohesion.

RQD = (Σ lengths of core pieces ≥100 mm / total run length) × 100; RQD <25% very poor, 25–50% poor, 50–75% fair, 75–90% good, 90–100% excellent rock mass.

Rock mass rating RMR = sum of ratings for UCS, RQD, spacing, condition, groundwater, adjusted by orientation; RMR 81–100 = very good, 61–80 good, 41–60 fair, 21–40 poor, <21 very poor.

Blasting: powder factor = explosive mass / rock volume (kg/m³); bench blast design uses burden B ≈ 25–40 × hole diameter depending on rock; stemming length ≥ 0.7 × burden typically.

Ventilation: airflow quantity Q = A × v; Atkinson equation for mine airway pressure loss p = (k·L·P·Q²)/A³ where k = friction factor, L = length, P = perimeter, A = area.

Surveying: traverse closure error must be distributed by Bowditch (compass) rule - correction proportional to leg length; tacheometry uses stadia constants; correlation and resection fix underground stations.

Mineral processing: Gaudin–Schuhmann and Rosin–Rammler describe size distributions; comminution energy follows Bond's law W = 10·Wi·(1/√P80 − 1/√F80); concentration by gravity, flotation, magnetic and electrostatic separation.

Economics: NPV = Σ (Ct/(1+r)^t) − C0; payback, IRR where NPV = 0; stripping ratio = waste volume / ore volume; cut-off grade balances mining, processing and refining costs against metal price.

In-situ stress: vertical stress σv = γ·z (γ = unit weight of overburden); horizontal stress σh = K·σv, with K typically 0.5–3 depending on tectonics and Poisson effect (K = ν/(1−ν) for elastic lateral constraint).

Kirsch equations give stresses around a circular opening: tangential stress at the boundary σθ = 3σ1 − σ3 for the biaxial case; maximum boundary stress concentrates at the sides perpendicular to the major principal stress.

Rock support design uses the Q-system: Q = (RQD/Jn) × (Jr/Ja) × (Jw/SRF); Q ranges map to support classes from unreinforced (Q > 40) to heavy support (Q < 0.1).

Shaft sinking: wall thickness and lining design from Lame's thick-cylinder equations; freezing, cementation and caisson methods handle water-bearing strata.

Drift development cycle: drill, blast, muck, support, ventilate, extend services; advance rate limited by pull per blast and cycle time; burn cut or wedge cut for hard rock faces.

Roof bolting: suspension, beam-building and keying mechanisms; bolt length commonly 1.5–2.5 m in coal, longer in hard rock; resin or mechanical anchors; mesh and shotcrete for surface retention.

Subsidence: angle of draw, critical width-to-depth ratio; trough subsidence profile described by influence functions; prediction matters for surface structures and water bodies.

Slope stability: factor of safety F = resisting forces / driving forces; planar failure when a discontinuity dips out of the face at angle less than slope angle; wedge and circular failures analysed by limit equilibrium.

Underground coal: bord-and-pillar (room-and-pillar) for shallow flat seams, longwall for deep seams; longwall panel width and face advance determine subsidence and production rate.

Underground metal: stoping methods - open stoping, sublevel stoping, cut-and-fill, shrinkage, sublevel caving, block caving; selection depends on ore strength, wall rock strength, dip and grade.

Block caving requires rock mass cavability; draw control and dilution management are critical; ore handling by grizzlies, chutes and LHD units.

Surface coal: strip mining with dragline or shovel-truck; dragline selection by boom length, bucket capacity and spoil pile reach; highwall stability governs stripping depth.

Open-pit design: bench height, bench width, berm width, overall slope angle; pit limits from Lerchs–Grossmann or floating cone optimisation; haul road grade typically 8–10%.

Placer and alluvial mining: hydraulic mining, dredging and sluicing; gold recovery by gravity concentration; environmental controls for tailings and water.

Solution mining and in-situ leaching for salt, potash, uranium and copper; well pattern, permeability and lixiviant chemistry control recovery.

Mine planning sequence: orebody modelling, pit or stope optimisation, production scheduling, equipment selection and ventilation/power design; cut-off grade links reserve to price.

Rotary drilling for soft rock, percussive for hard rock; penetration rate depends on bit load, rotation speed, flushing and rock abrasivity; specific energy minimised near optimal thrust.

Explosive properties: velocity of detonation (VOD), density, strength, water resistance, fume class; ANFO is cheap and dry-hole only; emulsion and slurry are water-resistant.

Charge calculations: explosive mass per hole = charge length × cross-section × density; powder factor = total explosive / broken rock volume; typical bench PF 0.3–1.0 kg/m³.

Delay sequencing: short-delay detonators in millisecond intervals improve fragmentation and reduce vibration; maximum instantaneous charge controls ground vibration.

Blast vibration: peak particle velocity predicted by scaled distance, v = K·(D/√Q)^−b; damage thresholds depend on structure type and frequency.

Controlled blasting: pre-splitting, smooth blasting and trim blasting protect final walls; reduced charge concentration and closer spacing along the wall line.

Misfire handling: follow site procedure, never redrill a misfired hole; safety fuse, detonating cord and electronic detonators each have specific handling rules.

Fragmentation assessment: image analysis (e.g., size distribution curves) and crusher throughput; oversize requires secondary breaking, adding cost.

Air quantity: Q = A·v; regulatory minimum air velocity and per-person air quantity (commonly 0.1–0.2 m³/s per person in Indian coal mines) must be met at the workplace.

Atkinson equation: p = (k·L·P·Q²)/A³; equivalent orifice and fan characteristic curves determine operating point at the intersection of fan and mine resistance curves.

Fan laws: Q ∝ N, p ∝ N², power ∝ N³ for a given fan and system; natural ventilation pressure from air density difference between intake and return shafts.

Mine gases: methane (CH4) explosive 5–15% in air; carbon monoxide toxic; hydrogen sulphide and sulphur dioxide irritant; oxygen deficiency below 19.5% is dangerous.

Heat and humidity: wet-bulb temperature governs heat stress; cooling capacity required = mass flow × specific heat × temperature drop plus latent load.

Dust control: respirable dust <5 µm reaches alveoli; silica causes silicosis; control by water spray, ventilation, filters and personal protective equipment.

Mine fires: spontaneous combustion of coal from oxidation; detection by CO/CO2 ratio and temperature; sealing, inertisation and nitrogen flushing are control methods.

Methane drainage: pre-drainage boreholes and goaf drainage reduce gas content; gas monitoring and automatic power cut-off at threshold concentrations.

Haulage: locomotive and rope haulage calculations use tractive effort, gradient resistance (1% grade ≈ 10 kg/t) and rolling resistance; brake path and rope safety factor ≥ 6 typically.

Conveyors: capacity Q = A·v·ρ (belt cross-section × speed × bulk density); belt tension, idler spacing and drive power from friction and lift components.

Hoisting: drum and friction (Koepe) winders; skip and cage payload; rope safety factor, acceleration limits and braking distances are statutory checks.

LHD and shuttle car cycle time = load + haul + dump + return; productivity = bucket payload × trips per hour × availability.

Pumps and drainage: head = static lift + friction loss; pump power P = ρ·g·Q·H/η; series for head, parallel for discharge.

Surveying instruments: total station measures horizontal and vertical angles plus slope distance; levels establish reduced levels; GPS/GNSS for surface control.

Underground correlation: plumbing shafts, Weiss quadrilateral, and gyrotheodolite orientation transfer azimuth from surface to underground.

Errors and adjustments: traverse angular misclosure distributed equally, linear misclosure by Bowditch rule; least-squares adjustment for precise networks.

Comminution: crushing and grinding reduce size; energy laws - Rittinger (n=2, surface), Kick (n=1, volume), Bond (n=1.5); Bond work index Wi from laboratory ball mill test.

Screening and classification: efficiency = (mass of undersize in product)/(mass of undersize in feed); hydrocyclone cut size depends on diameter, pressure and pulp density.

Gravity concentration: jig, shaking table, spiral and heavy-medium separation; separation by specific gravity difference; efficiency measured by Tromp curve and probable error.

Flotation: collectors, frothers, depressants and activators; pH and pulp potential control selectivity; xanthates for sulphides, amines for silicates, fatty acids for oxides.

Magnetic and electrostatic separation: low-intensity for magnetite, high-intensity for weakly magnetic minerals; electrostatic for dry conductors versus non-conductors.

Dewatering: thickening by settling (free and hindered), filtration by pressure or vacuum; moisture content affects transport cost and smelter penalties.

Hydrometallurgy: leaching (heap, tank, in-situ), solvent extraction, ion exchange and electrowinning; pyrometallurgy: roasting, smelting, converting and refining.

Metallurgical accounting: recovery = (concentrate mass × grade)/(feed mass × feed grade) × 100; two-product formula for concentrate grade from feed, concentrate and tailings assays.

Project evaluation: NPV = Σ Ct/(1+r)^t − C0; IRR sets NPV = 0; discounted payback; sensitivity analysis on grade, price and cost.

Costs: capital (capex) versus operating (opex); unit cost per tonne mined or milled; break-even grade and cut-off grade from price minus treatment and refining charges.

Reserves: measured, indicated and inferred resources under reporting codes; reserve = resource economically mineable after dilution and recovery.

Depreciation methods: straight-line, declining balance and sum-of-years-digits; depletion allowance for mineral deposits in some jurisdictions.

Safety statistics: frequency rate = (number of reportable injuries × 1,000,000)/man-hours worked; severity rate uses days lost per 1,000 man-hours.

Legislation: mine opening, manager appointment, statutory examinations, ventilation and dust standards, explosives licensing, and reporting of accidents are typically prescribed by national mining regulations.

Risk management: hazard identification, risk matrix (likelihood × consequence), hierarchy of controls from elimination to PPE; emergency response and mine rescue arrangements.

Environmental management: environmental impact assessment, tailings dam design, acid mine drainage prevention, mine closure and reclamation planning.