Question 5 of 7: Air Blast

Question 5: Air Blast (20 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) Parameters affecting air blast

Charge weight per delay – the dominant variable; overpressure scales with (charge/delay)^1/3-scaled distance, so splitting a round into more, smaller delays is the single most effective airblast-reduction tool; stemming length and quality – short or poor stemming releases gas directly to atmosphere, sharply raising airblast; confinement/burden adequacy – under-confined charges (too little burden, or venting through a nearby free face/joint) generate a strong air-coupled pulse; distance and atmospheric propagation path – wind direction/speed and temperature inversions can focus or amplify overpressure kilometres downwind; topography between source and receiver (line-of-sight vs. shielded by a ridge); and delay scatter/timing – charges that inadvertently overlap (fire within the same ≈8 ms window) are treated by the propagation physics as one larger simultaneous charge.

(b) Implications of the pressure-time record frequency content

Air-overpressure pulses from blasting are typically very low frequency (a few Hz down to sub-1 Hz for the main gas-release pulse), which is below the flat-response range of many standard sound-level meters optimised for the audible 20 Hz–20 kHz range; a meter or transducer with poor low-frequency response under-reads the true peak overpressure. This is why blast air-overpressure is measured with specialised, linear (unweighted) microphones/transducers with response down to ≈2 Hz rather than A-weighted sound meters, and why the peak (not an averaged/weighted) pressure is reported and compared against regulatory limits – the frequency content also determines whether the pulse couples efficiently into structures (window/wall resonance), which is the actual complaint mechanism in most nuisance cases.

(c) Overpressure design at 250 m – loading and delay recommendation

Given. Bench H=17 m, De=102 mm, ANFO ρ=0.85 g/cm³, B=3.0 m, S=4.0 m, stemming T=2.2 m, R=250 m; limit 128 dB; P=6(R/W^1/3)^-1.1; dB=20log(P_r/P₀), P₀=2×10^-8 kPa. No subdrill is stated for this hole, so the charge column is taken as the full hole length below stemming (H−T) – check.

Find. Whether the current per-hole charge (fired as one delay) meets the 128 dB limit at 250 m, the maximum allowable charge mass per delay W_max, and how to load/deck every hole to comply, with a recommended delay interval.

Approach. Compute the existing full-column charge per hole, convert the 128 dB limit to a kPa ceiling, invert the given attenuation law for W_max at R=250 m, then compare to the existing per-hole charge to size the required deck split.

1. Current charge per hole. Area(102 mm)=0.008171 m²; charge length = H−T = 17−2.2 = 14.8 m. $$Q_{hole}=14.8\times0.008171\times850=102.8\ \text{kg}$$
2. Current overpressure at 250 m (whole hole on one delay). $$P=6\left(\frac{250}{102.8^{1/3}}\right)^{-1.1}=0.0755\ \text{kPa} \;\Rightarrow\; dB=20\log\!\left(\frac{0.0755}{2\times10^{-8}}\right)=131.5\ \text{dB}$$ – this exceeds the 128 dB complaint limit, confirming the redesign is needed.
3. Convert the 128 dB limit to a pressure ceiling and solve for W_max. $$P_{limit}=2\times10^{-8}\times10^{128/20}=0.0502\ \text{kPa}$$ $$0.0502=6\left(\frac{250}{W^{1/3}}\right)^{-1.1}\;\Rightarrow\; \boxed{W_{max}=33.8\ \text{kg per delay}}$$
4. Size the deck split. 102.8/33.8 = 3.04, so a 3-way deck (34.3 kg/deck) still marginally exceeds W_max; a 4-deck split gives 102.8/4 = 25.7 kg/deck, comfortably under the 33.8 kg ceiling with margin for delay-scatter overlap.

Loading procedure. Split each 14.8 m charge column into four charges of about 3.7 m of ANFO (25.7 kg) each, separated by short (≈0.5–1.0 m) inert stemming plugs between decks in addition to the 2.2 m surface collar stemming, with each deck primed and initiated on its own delay number so that no single detonation event ever exceeds ≈ 30 kg.

Delay time recommendation. The 8 ms window is the recognised threshold (USBM RI 8507) below which two charges are treated as effectively simultaneous by the attenuation physics; to stay clear of that threshold with practical margin – and to give each deck's gas venting/rock movement time to relieve before the next deck fires – a 25 ms inter-deck/inter-hole delay is recommended (a standard surface delay interval), sequenced deck-by-deck down each hole and hole-to-hole across the pattern; this also keeps the whole round's maximum instantaneous charge at the single-deck value used above, since no two decks anywhere in the round share a delay number. Given the number of individual delay periods required (4 per hole across the round), electronic detonators are recommended over a fixed pyrotechnic delay series to provide the necessary number of discrete, accurate delay times.