PE Mining cheat sheet

Cutoff grade c = (mining + processing + refining + G&A costs) / (metal price × recovery × payable factor).

NSR = Σ(grade_i × recovery_i × price_i × payable_i) − treatment and refining charges.

Break-even stripping ratio = (ore value per tonne − ore mining and processing cost per tonne) / waste mining cost per tonne.

Room-and-pillar recovery = mined area / total area; pillar strength is estimated empirically and recovery commonly falls in the 50–70% range.

Longwall mining gives high extraction and controlled subsidence; it requires a continuous moving face with hydraulic roof supports.

Open pit versus underground selection depends on depth, orebody geometry, grade, stripping ratio, and geotechnical conditions.

Planning hierarchy: life-of-mine strategic plan, five-year tactical plan, and weekly operational plan; reserves are the mineable subset of resources.

Dilution lowers grade and ore loss reduces recovery; both are modeled explicitly in stope and phase design.

RMR sums scores for UCS, RQD, joint spacing, joint condition, and groundwater; 0–20 is very poor and 81–100 is very good.

Q = (RQD/Jn)(Jr/Ja)(Jw/SRF); Q values span roughly 0.001 to 1000 and guide support selection.

GSI estimates rock mass strength from blockiness and joint condition; Hoek-Brown parameters include mb = mi exp((GSI−100)/(28−14D)).

Pillar stress is often estimated as γH × (total area / pillar area); pillar factor of safety = pillar strength / pillar stress.

The subsidence angle of draw defines the surface influence zone above extraction and depends on rock mass, depth, and geometry.

Support systems include rock bolts, mesh, shotcrete, and steel sets; selection is tied to RMR, Q, span, and expected stand-up time.

Slope factor of safety = resisting forces / driving forces; groundwater pressure reduces effective stress and lowers slope stability.

Ground monitoring includes convergence stations, extensometers, piezometers, and microseismic arrays.

Powder factor = explosive mass / blasted rock volume or tonnes; it links blast design to fragmentation and cost.

Burden is the distance from a hole to the nearest free face; spacing is commonly set at 1.0–1.5 times burden.

Stemming length is typically about 0.7–1.0 times burden and reduces flyrock and airblast by confining gases.

Charge mass per hole = explosive density × loaded length × hole cross-sectional area × loading efficiency.

Millisecond delays between holes and rows change free-face conditions and influence fragmentation, vibration, and muckpile shape.

Presplit and smooth blasting use closely spaced, lightly charged perimeter holes to protect the final wall.

Airblast and vibration are assessed with scaled distance; vibration often uses SD = D/√Q and airblast uses D/Q^(1/3).

A misfire is handled by stopping work, marking the area, clearing fumes, and removing the charge under controlled procedures.

Atkinson equation: ΔP = R Q²; resistance R depends on friction factor k, airway length L, perimeter P, and area A as R = kLP/A³.

Series airways add resistance: R_eq = ΣR_i; parallel airways satisfy 1/√R_eq = Σ(1/√R_i).

Fan laws: airflow varies with fan speed, pressure with speed squared, and shaft power with speed cubed.

Air quantity Q = A × V; required airflow is set by personnel, diesel equipment, dust, gas, and heat loads.

Methane is explosive at roughly 5–15% by volume in air; dilution, monitoring, and drainage are key controls.

Respirable dust control uses water sprays, ventilation, filtration, and enclosure; silica-bearing dust causes silicosis.

Heat and humidity are managed with airflow, refrigeration, insulation, and limiting time in hot work areas.

Environmental controls include acid mine drainage prevention and treatment, tailings management, and water balancing.

Bond equation: W = 10 Wi (1/√P80 − 1/√F80) kWh/t, with P80 and F80 expressed in micrometres.

Bond work index Wi is ore-specific; a higher Wi means more grinding energy is required.

Comminution increases liberation; the grade-recovery curve shows the trade-off between concentrate grade and recovery.

Froth flotation uses collectors to make target minerals hydrophobic and frothers to stabilize bubbles.

Gravity and dense-medium separation rely on density differences; they are common for coal and coarse heavy minerals.

Thickening and filtration dewater slurries, recover process water, and prepare tailings for transport or storage.

Conveyor mass capacity = belt cross-sectional area × belt speed × bulk density.

Truck cycle time = load + haul + dump + return + queue; it sets truck productivity and shovel-truck matching.

NPV = Σ CF_t/(1+r)^t − initial capital; a positive NPV creates value at the selected discount rate.

IRR is the discount rate at which NPV equals zero; it is compared with the hurdle rate.

Payback period is the time to recover initial capital from cumulative cash flow; discounted payback uses present values.

AISC includes cash costs, sustaining capital, royalties, and G&A; it is used to compare operating performance across mines.

LTIFR = lost-time injuries × 1,000,000 / hours worked.

Risk is commonly scored as likelihood × consequence in a risk matrix to rank hazards and controls.

Hierarchy of controls: eliminate, substitute, engineer, administrate, and PPE; higher-level controls are more reliable.

Health and safety controls address ground control, traffic management, explosives, dust, noise, diesel emissions, and emergency response.