Question 6 of 7: Ground Vibration

Question 6: Ground Vibration (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 ground vibration

Charge mass per delay – the dominant factor (PPV ∝ (W/R²)^0.65 roughly, per the square-root scaled-distance form used in part d); distance from source to receiver; propagation-path geology (rock stiffness/attenuation, faults, water table – can amplify or attenuate the wave); delay timing and scatter – charges that unintentionally overlap add constructively; confinement/coupling of the charge to the rock (a well-coupled, well-stemmed charge transmits more seismic energy than a poorly coupled one, even though it also fragments better); burden (too little burden increases the proportion of energy that couples to the ground rather than doing useful rock-breaking work); and local site response at the receiver (soil amplification, structure natural frequency – part b).

(b) Effect of vibration frequency on structural response

Structures – particularly residential buildings, with typical fundamental natural frequencies in the 4–12 Hz range for walls/floors – respond most severely when the blast vibration's dominant frequency is close to the structure's own natural frequency, producing resonant amplification of the response well above the free-field PPV. Low-frequency blast vibration (<10 Hz, typical of large-charge, long-delay-interval or distant blasts) is therefore disproportionately more damaging to structures than the same PPV delivered at high frequency (>40 Hz, typical of small, close-in charges), which is why modern vibration standards (e.g. USBM RI 8507) use frequency-dependent PPV limits rather than a single flat threshold.

(c) Is frequency a controllable blast parameter?

Yes, indirectly. Dominant vibration frequency is not set directly but is strongly correlated with charge mass per delay and distance: smaller charges per delay and/or shorter delay intervals tend to shift the dominant frequency higher (further from typical low-rise structure natural frequencies), while very large charges per delay, long propagation distances and soft/attenuating ground paths shift it lower. A blaster can therefore raise the dominant frequency – and so reduce structural response for a given PPV – by reducing charge weight per delay (more, smaller decks/holes per delay) and by choosing delay timing that avoids reinforcing the natural period of nearby structures.

(d) Vibration-limited blast design – iron ore, 270 mm holes

Given. Limit PPV=12 mm/s at R=350 m; De=270 mm; H=14 m; ANFO ρ=0.85 g/cm³; powder factor K=1.2 kg/m³; square pattern (B=S), 20 holes/row, 5 rows; corner blast, diagonal tie-in; iron ore (hard rock).

Find. Maximum charge mass per delay W_max, the resulting per-hole deck split, and a recommended initiation timing sequence.

Approach. (1) Back-solve the given PPV attenuation law for W_max at R=350 m. (2) Determine the square-pattern burden B from the given powder factor (using the standard S=B, J=0.3B, T=0.7B ratios) to get the actual per-hole charge mass. (3) Compare and deck the holes as needed; (4) lay out a corner-initiated diagonal-echelon delay sequence.

1. Solve for W_max at the 12 mm/s, 350 m limit. $$12=700\left(\frac{350}{\sqrt{W}}\right)^{-1.3}\;\Rightarrow\; \boxed{W_{max}=235.1\ \text{kg per delay}}$$
2. Back out the square-pattern burden from K=1.2 kg/m³. With Area(270mm)=0.05726 m², S=B, J=0.3B, T=0.7B: $$K=\frac{(H-0.4B)\,Area\,\rho}{B^2H}=1.2\;\Rightarrow\;\boxed{B=S=5.82\ \text{m}}$$ giving J=1.74 m, T=4.07 m, hole depth=15.74 m, charge length=11.67 m.
3. Per-hole charge mass. $$Q=11.67\times0.05726\times850=568.1\ \text{kg/hole}\quad(\text{check: } K=568.1/(5.82^2\times14)=1.20\ \text{kg/m}^3\ \checkmark)$$
4. Deck split. 568.1/235.1 = 2.42, so a 2-deck split (284 kg/deck) still exceeds W_max; a 3-deck split gives 568.1/3 = 189.4 kg/deck, safely under the 235.1 kg ceiling.
5. Round totals. 20×5 = 100 holes × 3 decks = 300 individual charges/delay periods; total explosive = 568.1×100 ≈ 56.8 t ANFO.

Timing sequence. Because the round is corner-initiated with diagonal tie-ins, the collar-firing sequence follows a diagonal echelon out from the corner hole: using a practical hole-to-hole delay of 25 ms along each diagonal and a row-to-row delay of 75 ms (toward the upper end of the typical 25–65 ms/row guideline range, appropriate for hard, competent iron ore, which needs a longer relief time than a soft/friable rock to move and relieve before the next row fires), the corner hole fires at t=0 and the far corner hole of the 20×5 pattern fires at roughly 20×25 + 4×75 = 800 ms into the round. Within each hole, the 3 decks fire on their own delay numbers spaced by the same ≥25 ms interval used between holes, so that at no instant does the total detonating charge exceed the single-deck value (189.4 kg < 235.1 kg W_max). This requires 300 individually numbered delay periods across the round, only practically achievable with programmable electronic detonators rather than a fixed pyrotechnic series.