Depth-

Overburden σv-

Pillar load σp-

Safety factor-

Airflow-

CH₄ at face-

Pillar safety factor

<11.31.62.2+

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Underground Mine Cutaway Blender 5.2

Pillar stress, skip hoist and ventilation in one working mine. Drag to orbit, pinch or wheel to zoom, right-drag to pan.

Presets

Ground control: pillars and overburden

Rock Strength model

Overburden σv-

Pillar load σp-

Pillar strength-

Safety factor-

Room width b-

Pitch w+b-

w / h ratio-

Extraction-

Tributary area-

Load per pillar-

Strength rises with width; load at fixed room width falls as the pillars widen. The crossing with the dashed 1.6 line is the minimum design width.

Experiment: minimum pillar width

Question: how narrow can the pillars be, for the current room width and depth, and still keep the safety factor at the target?

Target FoS

The width slider will sweep up from 2 m while the layout is re-measured at every step, then the answer is compared with the closed-form cubic root.

Shaft hoisting

Hoisting distance-

Top speed reached-

Travel time-

Cycle time-

Hoisting rate-

Peak motor power-

RMS power-

Energy per tonne-

Rope safety factor-

Speed and motor power of the loaded skip during one trip (trapezoidal profile, a = 0.9 m/s²). Power starts high and falls as the rope weight transfers to the other skip.

Ore flow: face to surface

Face machine-

Shuttle trucks-

Crusher-

Skip hoist-

Slowest stage-

Bottleneck-

Measured (last h)-

Delivered-

Ventilation

Total airflow Q-

Fan pressure-

Air power-

Mine resistance R-

Panel A flow-

Panel B flow (face)-

Shaft velocity-

Face room velocity-

Methane at face-

Fan characteristic at the chosen speed (blue), rated curve (grey) and the mine's Atkinson curve p = R Q² (orange). Their intersection is the airflow.

View

Independent numerical checks

throughput: press "Skip ahead 1 h" in the ore-flow section to measure it

The science

Overburden stress

σv = ρ g H with ρ ≈ 2.3 to 2.75 t/m³, about 25 kPa per metre of depth: 6 MPa at 250 m, 40 MPa at 1.5 km. Horizontal stress and tectonics are ignored.

Tributary-area pillar stress

Each pillar carries the column of rock above its share of the panel: σp = σv (w+b)² / w² = σv / (1 − e) where e is the extraction ratio. This assumes an infinite regular grid of square pillars under a wide panel; edge pillars, rib spall, abutment stress and roof stiffness are neglected, so real pillars at the panel edge carry more.

Pillar strength

Empirical size-effect formulas, σs = σ1 (0.64 + 0.36 w/h) (Bieniawski) or σ1 (0.778 + 0.222 w/h) (Obert-Duvall), where σ1 is the strength of a 1 m cube of the rock mass. Squat pillars (large w/h) are stronger because confinement builds in the core. The σ1 values used (coal 7, salt 22, copper ore 48, gold reef 95 MPa) are illustrative. Safety factor FoS = σs / σp, designs usually target 1.5 to 2.

Skip hoisting

Trapezoidal speed profile with acceleration a and top speed v: T = H/v + v/a if the top speed is reached, otherwise T = 2√(H/a). Drum force F = m g + n w g (H − 2s) + k M a (payload, out-of-balance rope weight of a two-skip balanced winder, and inertia of everything that moves), power F v / η. Rope safety factor = breaking load / maximum static plus dynamic load, usually required to be ≥ 5. Rope mass 0.0045 d² kg/m and breaking load 0.8 d² kN (d in mm) are typical locked-coil figures. Cycle = travel + 14 s of simultaneous loading and dumping.

Ventilation

Turbulent mine airways follow Atkinson's law p = R Q², R = k P L / A³ (k friction factor, P perimeter, L length, A area). Parallel airways share the same pressure drop so 1/√R = Σ 1/√ri and each carries Qᵢ = √(Δp / Ri). A regulator is an orifice, R = ρ/(2 (Cc A)²). A fan obeys the fan laws (Q ∝ N, p ∝ N²) so its curve is p = s² p₀ [1 − (Q / (s Q₀))²]; setting it equal to R Q² gives Q = s √(p₀ / (R + p₀/Q₀²)). Methane is diluted by the air through the face room: c = q(CH₄) / Q(room). The drawn field is a representative section: 800 m of extra airway is added to each room for resistance. Natural ventilation pressure and leakage are neglected.

Ore flow

The chain face machine, shuttle trucks, crusher and skip hoist is a series of stock-flow stages with buffers (face pile, hopper, loading flask). The long-run throughput is the capacity of the slowest stage, which the simulation recovers by measurement. Truck capacity 30 t, speed 4 m/s, crusher 900 t/h. The animation compresses geometry (display scale 0.2 units per metre) but keeps real times for travel and hoisting; speed it up with the simulation-speed slider.

Educational model. It is not a mine design tool. No company or product is depicted. All structures are shown in normal operation.