Question 2 of 7: Scaling a Blast Pattern to a Larger Hole Diameter

Question 2: Scaling a Blast Pattern to a Larger Hole Diameter (15 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

(a) New pattern dimensions and loading for 165 mm holes

Given. D₁=102 mm, B₁=2.5 m, S₁=3.0 m, bench height H=12 m, ANFO ρ=850 kg/m³; new D₂=165 mm.

Find. B₂, S₂, and the charge per hole for the new diameter, holding average fragmentation (specific charge/powder factor) approximately constant.

Approach. To keep the same fragmentation, geometric similarity of the pattern is preserved: burden and spacing (and, by standard practice, subdrill and stemming) scale linearly with hole diameter, holding B/D, S/D, J/B and T/B constant, since linear charge concentration scales with D² while the rock volume broken per hole scales with B×S (∝D²) – the two track together and specific charge stays close to constant.

1. Scale burden and spacing. $$\frac{D_2}{D_1}=\frac{165}{102}=1.618$$ $$B_2=2.5\times1.618=\boxed{4.04\ \text{m}},\quad S_2=3.0\times1.618=\boxed{4.85\ \text{m}}$$
2. Linear charge concentration (charge per metre of hole). $$q_L=\frac{\pi}{4}D^2\rho_{ANFO}$$ $$q_{L,1}=\frac{\pi}{4}(0.102)^2(850)=6.94\ \text{kg/m},\quad q_{L,2}=\frac{\pi}{4}(0.165)^2(850)=\boxed{18.18\ \text{kg/m}}$$
3. Subdrill and stemming (standard proportions, J=0.3B, T=0.7B – not given by the source, applied by standard practice): $$J_2=0.3(4.04)=1.21\ \text{m},\quad T_2=0.7(4.04)=2.83\ \text{m}$$ Hole length $$L_2=H+J_2=12+1.21=13.21\ \text{m}$$, charge length $$L_{c,2}=L_2-T_2=13.21-2.83=10.38\ \text{m}$$
4. Charge mass per hole. $$m_2=q_{L,2}\times L_{c,2}=18.18\times10.38=\boxed{188.7\ \text{kg/hole}}$$
5. Check – powder factor before/after. $$PF_1=\frac{q_{L,1}(H+J_1-T_1)}{B_1S_1H}=\frac{76.4}{90.0}=0.85\ \text{kg/m}^3,\quad PF_2=\frac{188.7}{B_2S_2H}=\frac{188.7}{235.5}=0.80\ \text{kg/m}^3$$

(b) Controllable blast-design parameters affecting fragmentation

Burden and spacing – the dominant levers: tighter B/S concentrates more explosive energy per unit rock volume (finer fragmentation), while excessive burden under-breaks and produces boulders and toe problems. Hole diameter – sets the maximum practical burden and the explosive's linear charge concentration; larger diameters are more efficient per metre drilled but coarsen fragmentation unless burden/spacing are scaled up to compensate. Powder factor (specific charge) – the overall explosive energy per unit rock volume, the single strongest lever on mean fragment size. Stemming length and material – inadequate stemming vents gas energy prematurely and coarsens/loses fragmentation near the collar. Subdrill – ensures full-height breakage to grade; too little leaves toe humps (oversize at the floor). Delay timing and initiation sequence – proper delays create free-face relief for each successive row, improving fragmentation and reducing throw/vibration versus simultaneous or poorly sequenced firing. Explosive type/energy (VOD, density) – higher-energy, higher-density products (e.g., emulsion vs. ANFO) increase both shock and gas energy delivered to the rock. Deck/air-decking design – redistributes charge energy along the hole to better match the rock's confinement profile.