Vibration, Airblast and Flyrock at a 450 m Receptor

Assumptions. Site law of the form PPV = K·(D/√W)^(−B) with B = 1.6 (a common value for competent rock at these distances), D fixed at 450 m, and maximum charge per delay W as the controlling variable. The same law is assumed valid over the small range of W considered.

Required reduction. 8.2 → 5.0 mm/s is a factor of 1.64. Since PPV ∝ W^(B/2) = W^0.8, the charge per delay must fall by the factor 1.64^(1/0.8) = 1.64^1.25 ≈ 1.86. So W_max = 360/1.86 ≈ 194 kg per delay.

Check. 8.2 × (194/360)^0.8 = 8.2 × 0.61 ≈ 5.0 mm/s. Consistent.

Practical translation. At roughly 45 kg per hole, 194 kg means four holes per delay instead of eight. That doubles the number of delay groups and lengthens the blast, which is acceptable if timing is accurate. Increasing distance instead would need 450 × 1.36 ≈ 613 m, which the property boundary will not allow.

Why the engineer's proposal fails. Adding 25 ms shifts initiation timing but does not change the maximum charge detonating within an 8 ms window. If the existing 12 ms delays are firing with scatter - and non-electric delays routinely scatter by ±10% or more - holes intended as separate delays can effectively fire together, so the true charge per delay may already exceed 360 kg. That would explain why the measured value is 64% above the limit rather than near it.

Recommendation. Verify actual charge weight per delay with an electronic detonator or a high-speed video, cap it at four holes (or two decks of four), and re-monitor from the same location before any further production firing. A confirmatory shot at reduced charge is the cheapest possible test.

Diagnosis: inadequate confinement, in three compounding ways.

1. Burden deficiency. Measured front-row burden of 2.2 m against 3.0 m design is a 27% linear reduction, so the front row is carrying roughly 40% more explosive per cubic metre of rock than designed. The hole has less rock to move than it has energy to move it, and the excess energy leaves as flyrock in the direction of least resistance - toward the nearest receptor.
2. Weathered crest. Three metres of highly weathered andesite at the crest has low tensile strength and open joints, so it fails at low pressure and throws further than competent rock for the same energy.
3. Stemming shortfall. 2.5 m of stemming against a 3.0 m design burden is below the usual rule of thumb (stemming at least 0.7–1.0 × burden). Short stemming vents gas upward, which both throws collar rock and generates airblast.

Design changes.

• Measure and mark burden on every front-row hole with the laser profiler and adjust charge per hole to the measured burden, not to the design burden. Holes under a defined minimum burden are not loaded or are loaded lightly and blasted with the next row.
• Increase stemming to 3.0 m or more, using angular crushed rock rather than drill cuttings, which can flow out under gas pressure.
• Reduce explosive concentration in the front row (bottom-heavy charge distribution, decked charges, or a smaller-diameter front-row pattern).
• Move to electronic detonators so burden relief and timing are controlled rather than assumed.

Procedural changes.

• Re-survey the exclusion zone on the basis of a flyrock risk assessment rather than habit; 180 m of throw from 2.2 m burden should drive the zone to at least 250–300 m with mats over the front row.
• Inspect the front row after every blast for crest loss and update the profile.
• Stop blasting when the crest cannot be profiled or when the weathered zone has not been removed by pre-stripping.

Airblast. 124 dB(L) against a 120 dB(L) limit is a 4 dB exceedance, which is roughly a 60% increase in acoustic energy - audible and structurally relevant at a house 450 m away. Where does it come from?

• Exposed surface detonating cord or a lead-in line is the most common cause of a high dB(L) reading with a low-frequency signature; inspect the shot for uncovered trunkline.
• Short stemming vents gas directly; fixing stemming to 3.0 m plus proper stemming material is the second lever.
• Overcharging, particularly where burden is deficient, converts explosive energy to gas escape rather than rock breakage.
• Decking and electronic timing reduce the coincidence of gas release across the shot.

Target the same reduction logic as vibration: eliminate exposed cord, fix stemming, then re-monitor at the same residence with the same instrument, documenting calibration and trigger level.

The cracked plaster complaint.

1. Do not argue damage thresholds on site. The permit limit governs, and the blast exceeded it; that is the operative fact.
2. Commission a condition survey by an independent building assessor, with photographs and crack width measurement, and install crack monitors to establish whether movement is ongoing.
3. Retrieve the seismograph record for the specific event and check instrument calibration, sensor coupling to the foundation, and whether the monitoring point is actually at the nearest structure.
4. Record all subsequent blasts at the residence, not in the pit, and keep the records for the permit file.
5. Correct the design and prove the correction with a compliant monitored shot before resuming full production, and communicate the results to the resident in writing.

The engineering point to carry into the exam answer: a compliant blast design is demonstrated by monitored data at the receptor, not by a calculation sheet.