Open-Pit Design

An open pit is a stepped excavation whose walls must be steep enough to limit waste but safe from failure. Learn pit terminology (bench, berm, face, inter-ramp and overall slope angles), stripping ratios, breakeven stripping ratio, how ramps flatten the overall slope, and the pit design process.

Open pits produce most of the world's copper, iron ore, gold and coal. Some are over 1 km deep (Bingham Canyon ≈ 1.2 km). Every degree of wall slope matters: steepening a 500 m deep pit by 1° can save tens of millions of tonnes of waste — but a slope failure can bury equipment and people.

An analogy

An open pit is like a giant stadium carved into the ground: each row of seats is a bench, the aisles are haul ramps, and the steepness of the stands is the slope angle.

Pit anatomy

Benches (typically 10–15 m high) with faces at 60–80°, separated by berms that catch rockfall. Groups of benches between ramps form the inter-ramp slope; the whole wall from crest to toe is the overall slope. Haul ramps spiral or switch back from pit floor to the rim.

Stripping ratio economics

The overall SR measures total waste per ore. Each pushback (expansion) has an incremental SR; mining continues outward while incremental SR is below BESR. Low-grade ore needs a low SR; rich ore can bear more waste.

Design sequence

Block model → pit optimisation (ultimate pit shell) → nested shells and pushbacks → detailed design with benches, berms, ramps and geotechnical sectors → scheduling. Geotechnical engineers provide slope angles for each wall sector and rock type.

Slope risk

Steep slopes increase value but also failure probability; design uses factor of safety (≥ 1.2–1.3) and probability of failure (≤ 5–10 % bench, ≤ 1 % overall). Slope radar, prisms and InSAR monitor movement in real time.

Formulas

• Inter-ramp angle: tan θ_IRA = H_b / (H_b / tan α_f + B)
• Overall slope with ramps: tan θ_OSA = H / (H / tan θ_IRA + Σ ramp widths)
• Stripping ratio: SR = waste / ore
• Breakeven SR: BESR = (revenue − ore costs) / waste cost [per t ore]

Worked example: Inter-ramp angle

Given: Bench 15 m, face 70°, berm 8 m

Find: IRA.

• Horizontal per bench = 15/tan 70° + 8 = 5.46 + 8 = 13.46 m
• IRA = atan(15/13.46) = 48.1°

Answer: ≈ 48°

Worked example: Stripping ratio and BESR

Given: Pit: 30 Mt ore, 120 Mt waste; Ore value $40/t, ore costs $25/t, waste cost $2.5/t

Find: SR and BESR.

• SR = 120/30 = 4.0
• BESR = (40 − 25)/2.5 = 6.0

Answer: SR 4 < BESR 6 → profitable; can expand while incremental SR < 6

Common mistakes

• Wrong: Using the inter-ramp angle as the overall slope. — Right: Ramps and geotechnical berms flatten the overall slope.
• Wrong: Judging pit viability by overall SR only. — Right: Use incremental SR for each pushback.

Applications

• Copper and gold pits: Large pushback designs over decades.
• Iron ore: Shallow, extensive pits at very high production rates.
• Slope optimisation: Steepening walls using better geotechnical data.

Key takeaways

• Bench + face + berm → inter-ramp angle.
• Ramps flatten the overall slope.
• SR vs BESR decides pit limits.
• Balance slope steepness against risk.

Going further

• Probabilistic slope design: Probability of failure targets by consequence.
• In-pit crushing & conveying: Reduces truck haulage and ramp requirements.
• Slope monitoring: Radar and InSAR give early warning of failures.