🎓 Lesson 11
D5
Cavity-Hour Tooling Rate Formula
The Cavity-Hour Tooling Rate Formula calculates how much time a drilling machine spends creating blast cavities (holes) per hour, helping engineers plan tooling costs and equipment productivity.
🎯 Learning Objectives
- ✓ Calculate cavity-hour tooling rate given drill parameters, rock properties, and operational data
- ✓ Analyze how bit type and rock abrasivity affect cavity-hour rate using industry-standard wear factors
- ✓ Apply the formula to compare tooling efficiency across different drill rigs and bit configurations
- ✓ Design a tooling budget for a blasting campaign by converting cavity-hour rates into consumable cost per m³
📖 Why This Matters
In surface mining, up to 30% of total blasting cost stems from drill bit and rod consumption—not just fuel or labor. Traditional 'meters-per-hour' metrics ignore that drilling a 165 mm hole in quartzite yields far less usable cavity volume (and incurs higher wear) than the same length in weathered sandstone. The Cavity-Hour Tooling Rate bridges this gap: it measures *productive cavity volume per hour*, enabling accurate machine hour rate allocation, realistic tooling budgets, and fair comparison between rotary blasthole drills and down-the-hole (DTH) rigs. Without it, engineers risk underestimating bit costs by 2–4×—a critical error when bidding contracts or optimizing fleet utilization.
📘 Core Principles
Cavity-Hour Tooling Rate rests on three foundational concepts: (1) Cavity volume is the geometric volume of the blast hole (πr² × depth), not linear length—this accounts for energy transfer efficiency and fragmentation potential; (2) Effective drilling time excludes non-productive delays (bit changes, repositioning, surveying), so only 'cavity-creating' seconds count; (3) Tool wear is inherently volume-dependent—not time-dependent—so correlating wear to m³ drilled (not hours or meters) aligns with empirical bit life data from manufacturers like Sandvik and Boart Longyear. Advanced applications integrate Rock Mass Rating (RMR) and Protodyakonov hardness (f-value) to adjust base rates via wear multipliers, recognizing that a single hour in f=12 granite degrades a tungsten-carbide bit as much as 3.2 hours in f=4 limestone.
📐 Key Calculation
The Cavity-Hour Tooling Rate (CHR) expresses productive cavity volume per effective drilling hour. It requires measured penetration rate, hole geometry, and verified uptime. Use it to benchmark drill performance, forecast bit replacement intervals, and allocate consumable costs to blasted tonnage.
Cavity-Hour Tooling Rate (CHR)
CHR = Σ(V_cavity) / T_effectiveMeasures productive blast cavity volume generated per effective machine hour.
Variables:
| Symbol | Name | Unit | Description |
|---|---|---|---|
| CHR | Cavity-Hour Tooling Rate | m³/hr | Productive cavity volume per effective drilling hour |
| V_cavity | Cavity Volume per Hole | m³ | π × (hole radius)² × hole depth |
| T_effective | Effective Drilling Time | hr | Total time spent actively penetrating rock across all holes |
Typical Ranges:
f=4–6 sedimentary rock, 165 mm DTH: 1.1 – 1.6 m³/hr
f=10–12 granite, 165 mm DTH: 0.65 – 0.85 m³/hr
f=14+ quartzite, 165 mm DTH: 0.45 – 0.60 m³/hr
💡 Worked Example
Problem: A Sandvik DR400 drills 165 mm diameter holes to 12.5 m depth in granite (f = 10). Average penetration rate = 0.85 m/min. Bit change time = 8 min per hole. Survey & move time = 5 min/hole. Total holes drilled in 8-hour shift = 14. Calculate CHR.
1.
Step 1: Compute cavity volume per hole: π × (0.0825 m)² × 12.5 m = 0.277 m³/hole
2.
Step 2: Compute total cavity volume: 14 holes × 0.277 m³ = 3.878 m³
3.
Step 3: Compute effective drilling time: Penetration time = 12.5 m ÷ 0.85 m/min = 14.71 min/hole → 14 × 14.71 = 205.9 min. Total non-productive time = 14 × (8 + 5) = 182 min. Total shift time = 480 min → Effective drilling time = 480 − 182 = 298 min = 4.97 hrs
4.
Step 4: Apply formula: CHR = 3.878 m³ ÷ 4.97 hr = 0.780 m³/hr
5.
Step 5: Verify against typical range: For f=10 granite with 165 mm DTH bit, typical CHR = 0.65–0.85 m³/hr → 0.780 falls within acceptable range.
Answer:
The Cavity-Hour Tooling Rate is 0.780 m³/hr, confirming efficient operation within expected bounds for this rock-bit combination.
🏗️ Real-World Application
At Newmont’s Boddington Mine (Western Australia), engineers replaced legacy 'm/hr' KPIs with CHR during a fleet optimization study. By measuring cavity volume (not just depth) and isolating bit-wear time, they discovered their fleet’s average CHR was 0.52 m³/hr in fresh porphyry (f=14)—22% below design spec. Root cause analysis revealed undersized DTH hammers causing excessive bit slugging. After upgrading to high-energy hammers and adjusting air pressure, CHR increased to 0.64 m³/hr, extending bit life by 37% and reducing consumable cost per tonne by A$0.18—yielding A$2.3M annual savings across 12 drills. This case is documented in the 2022 AusIMM Blasting Best Practices Handbook.