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Vibration Limit, Fragmentation and a Village at 100 m

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Vibration Limit, Fragmentation and a Village at 100 m

A 100 mm hole open-pit blast (8 m bench, 3.5 m burden, 3.0 m spacing, 42 kg emulsion per hole, 25 ms pyrotechnic delays) is 100 m from a village. Your seismograph at the nearest house records 14 mm/s peak particle velocity, and the site-specific regression from 20 monitored events is PPV = 700 x SD^(-1.5), where SD = distance (m) / square root of charge weight per delay (kg). The regulator's limit at the house is 5 mm/s. Complaints are also about dust and airblast. Meanwhile the excavator operator reports coarse fragmentation, with 600 mm boulders and slow mucking. Hole cost is $18/m, emulsion $3.20/kg, rock density 2.6 t/m3, and the excavator/truck fleet is the bottleneck in a low-margin pit running about 2 Mt/y.

1. Calculate the maximum charge weight per delay allowed at the nearest house and state what must change.

Read the worked answer

Solve the site law for 5 mm/s

  • 5 = 700 x SD^(-1.5) -> SD^1.5 = 140 -> SD = 140^(2/3) = 26.9
  • SD = D / sqrt(W) -> sqrt(W) = 100 / 26.9 = 3.71 -> W = 13.8 kg per delay

What must change The blast is running 42 kg on a single 25 ms delay - roughly three times the permitted charge per delay. You need at least three times as many delays, or decked charges, to get each charge down to about 13-14 kg (a 13 kg charge gives SD = 27.7 and PPV about 4.8 mm/s).

Judgement the exam expects

  • The regression is empirical: the constant scatters with geology, confinement and direction. Trial the new design with seismographs at the house and at an intermediate point, and treat 13.8 kg as a starting point, not a guarantee.
  • Check airblast (about 133 dB / 0.1 psi at the house) and dust as separate criteria - they are often the binding constraint near a village, not PPV.
  • Timing windows and community notification are part of the control, not an afterthought.

2. You also need finer fragmentation. How do you get a higher powder factor while cutting charge per delay by two-thirds?

Read the worked answer

The two goals look contradictory only if you keep the same hole. Current powder factor = 42 kg / (3.5 x 3.0 x 8 x 2.6 = 218 t) = 0.19 kg/t, which is low and explains the 600 mm boulders.

Decouple powder factor from charge per delay

  1. Smaller diameter, tighter pattern. Move to 76 mm holes at roughly 2.2 m burden x 2.0 m spacing: about 91 t per hole. A 4.5 m column of 1.25 g/cm3 emulsion holds about 25 kg, giving about 0.28 kg/t - a 50% powder factor increase with a smaller charge per hole than today.
  2. Deck the holes. Split each 25 kg column into two 12.5 kg decks separated by 10-20 ms in-hole. Each deck is then inside the 13.8 kg limit (SD = 28.3, PPV about 4.6 mm/s) while the hole as a whole delivers the energy.
  3. Electronic detonators. Accurate 8-10 ms delays let you fire more holes and more decks within one blast without the scatter and truncation of pyrotechnic timing, which improves fragmentation and keeps each individual charge small.
  4. Supporting changes: reduce subdrill and improve stemming to cut overpressure; water the muck and blast during agreed hours for dust.

Net: more drilling metres and slightly more explosive per tonne, bought in exchange for a compliant PPV and better dig rates.

3. Is the finer fragmentation worth the added cost? How do you settle it?

Read the worked answer

Rough the numbers up

  • Current drilling: 8 m per 218 t = 0.037 m/t x $18/m = $0.66/t
  • Proposed drilling: 8 m per 91 t = 0.088 m/t at, say, $15/m for the smaller hole = $1.31/t
  • Explosive: +0.09 kg/t x $3.20 = +$0.29/t
  • Net extra cost is roughly $0.9-1.0/t of ore, about $1.8-2.0 M/y at 2 Mt/y.

Against that If the excavator/truck fleet is genuinely the constraint, a 10% dig-rate improvement on 2 Mt/y releases about 200 kt of extra mill feed; at an $8/t margin that is about $1.6 M - less than the added cost. The case is close and could go either way, and it hinges on the real cycle-time gain and on secondary-breakage hours, not on opinion.

So settle it with a trial, not an argument

  • Run a full-scale trial on one bench: measure dig cycle time, secondary breakage hours, crusher throughput, fragmentation image analysis, and PPV/airblast at the house.
  • Interrogate the dominant cost term - drilling. Consumables price, bit life in the new diameter, and whether a longer hole with decking can thin out the pattern all matter more than the blast design debate.
  • Only commit the fleet-wide change once the trial shows a downstream gain that beats the $0.9-1.0/t cost with margin.