Question 6 of 6: Quarry Blast Vibration-Compliant Loading Design

Question 6: Quarry Blast Vibration-Compliant Loading Design (21 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) Vibration-compliant loading, 2 rows × 12 holes, limit 6 mm/s at 500 m

Given.

Find. The maximum charge mass per delay, W_max, that keeps PPV ≤ 6 mm/s at 500 m, and how to load/deck/time the 24 holes to respect it.

Approach. Invert the given attenuation law for W at the limit; compute the full-column charge for one 165 mm hole using standard diameter-based burden/stemming/subdrill ratios (not otherwise given); compare and deck if the full charge exceeds W_max.

1. Solve for W_max. $$6=774.9\left(\frac{500}{\sqrt{W}}\right)^{-1.327}\ \Rightarrow\ \frac{500}{\sqrt{W}}=\left(\frac{774.9}{6}\right)^{1/1.327}=39.0$$ $$\sqrt{W}=\frac{500}{39.0}=12.8\ \Rightarrow\ \boxed{W_{max}=165\ \text{kg per delay}}$$

2. Full-column charge in one 165 mm hole. No burden/stemming is given, so use standard diameter-based design ratios: burden B≈30×De=4.95 m, stemming T≈20×De=3.30 m, subdrill≈8×De=1.32 m. Charge length = H+subdrill−T = 12+1.32−3.30=10.02 m; area = 0.02138 m²: $$Q_{hole}=10.02\times0.02138\times800=\boxed{171\ \text{kg}}$$ – a single hole fired instantaneously (171 kg) exceeds W_max (165 kg), so the hole must be decked rather than fired as one full-column charge.
3. Deck the charge. $$n_{decks}=\left\lceil\frac{171}{165}\right\rceil=2,\qquad \boxed{85.7\ \text{kg per deck}}$$ Two roughly-equal decks per hole (85.7 kg each), separated by an inert stemming plug, each fired on its own delay number – both stay comfortably under the 165 kg ceiling with margin for delay scatter.

Sequence and timing. With 24 holes each split into 2 decks (48 charge events), sequence the round so that no two decks anywhere in the pattern share, or fall within ≈8 ms of, the same delay number (Q1(j)) – e.g. a diagonal echelon stepping hole-by-hole and deck-by-deck at a nominal 25 ms interval from the corner closest to the open face. This keeps the instantaneous per-delay charge at the single-deck value (85.7 kg, well under the 165 kg ceiling) for every event in the round, while giving each row time to relieve into the void left by the row ahead of it.

(b) Will the design eliminate complaints? Additional steps

Meeting the 6 mm/s PPV limit reduces the risk of any real structural concern, but it does not guarantee zero complaints – human perception of blast-induced vibration and airblast is far more sensitive than the regulatory damage threshold (people routinely notice and are annoyed by ground motion and air overpressure well below levels that threaten structures), and low-frequency rattle, dust, and simply the unpredictability of blast timing are common complaint drivers independent of measured PPV. Additional steps: maintain margin below the 6 mm/s limit rather than designing exactly to it (delay scatter and geological variability can push an individual shot above a tightly-designed value); control airblast with adequate stemming and by avoiding uncovered detonating cord/exposed trunklines; blast at consistent, pre-announced times of day; issue pre-blast notifications to nearby residents; conduct a pre-blast survey of nearby structures (baseline documentation protects both the operator and residents); operate continuous, third-party-auditable vibration and airblast monitoring with results available on request; and provide a complaint hotline/log so recurring nuisance patterns (rather than just regulatory exceedances) can be identified and addressed proactively (e.g. shifting the blast time, adding a delay stage, or increasing decking further even though already compliant).