Question 3 of 6: Tunnel Round Design – Wall Control and Cut

Question 3: Tunnel Round Design – Wall Control and Cut (15 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) Wall (perimeter) hole design for smooth blasting

Given. Drift 6 m × 4.7 m, wall holes De=51 mm, emulsion cartridges 17/25/32/40/45 mm, ρ=1.15 g/cm³, ideal VOD=5500 m/s.

Find. Decoupled cartridge diameter, linear charge concentration, perimeter spacing/burden, and timing/detonator choice for a smooth-blasting perimeter.

Approach. Wall-control (smooth blasting) works by using a small, decoupled charge that generates a controlled radial pressure well below the rock's dynamic crushing strength but enough to propagate a clean shear crack between adjacent holes – select the smallest available cartridge, check the resulting borehole pressure via the decoupling relation, then size spacing from the standard S=12×De guideline.

1. Explosive detonation pressure. $$P_d=\frac{\rho\,VOD^2}{4}=\frac{1.15(5.5)^2}{4}=8.70\ \text{GPa}$$
2. Decoupled borehole pressure, smallest cartridge (17 mm in a 51 mm hole). $$\frac{d_c}{d_h}=\frac{17}{51}=0.333,\qquad P_b=P_d\left(\frac{d_c}{d_h}\right)^{2.4}=8.70(0.333)^{2.4}=\boxed{0.623\ \text{GPa}}$$ – a large reduction from the 8.70 GPa fully-coupled pressure, exactly the controlled, low-intensity loading smooth blasting needs.
3. Linear charge concentration and spacing. $$q_L=\frac{\pi}{4}(0.017)^2(1150)=0.261\ \text{kg/m},\qquad S=12\,D_h=12(0.051)=\boxed{0.612\ \text{m}}$$ with burden to the nearest production/buffer hole $$B\approx S/0.8=0.765\ \text{m}$$ (standard smooth-blasting S/B≈0.8 guideline).

Sequencing and detonator choice. The wall (perimeter) row must fire after the production/cut rounds of the same face round have already broken and relieved toward the opening – it is timed on the last delay of the round so it is trimming an already-relieved face rather than cratering into intact rock, which is what keeps its own low-energy charge effective at producing a clean shear line rather than just bruising the wall. Adjacent perimeter holes are fired on the same delay number (or the smallest available delay increment) so the crack propagates simultaneously along the whole contour rather than hole-by-hole, which would leave a jagged, overbroken profile. Non-electric (shock-tube/Nonel) detonators are the optimum choice underground for this application: they give the simultaneous, low-cost, large- channel-count initiation the perimeter row needs, are immune to the stray-current and static hazards of electric detonators (a real risk near mining electrical equipment), and are far cheaper per hole than electronic detonators for a role (simultaneous perimeter firing) that does not need electronic timing's fine millisecond resolution – that resolution is better spent on the cut and production holes instead (Question 3(b) below).

(b) Cut design with 75 mm relief hole

Given. Face 6 m × 4.7 m, empty (uncharged) relief hole Ø₀=75 mm, 51 mm charged production holes with the same 17-45 mm emulsion cartridge range.

Find. A parallel-hole (Holmberg-type) burn-cut design around the empty hole – successive charged-hole burdens, loading and firing sequence.

Approach. A parallel/burn cut breaks outward from the single large uncharged relief hole in successive square "rings," each new ring's burden set by the standard rule of thumb a₁=1.5Ø₀ for the first ring, then a_i+1=1.5√2·a_i for each following ring (the √2 factor keeps each new burden geometrically consistent with the growing square void left by the rings fired before it).

1. Ring burdens. $$a_1=1.5(0.075)=\boxed{0.113\ \text{m}}$$ $$a_2=1.5\sqrt{2}\,a_1=1.5(1.414)(0.113)=\boxed{0.239\ \text{m}}$$ $$a_3=1.5\sqrt{2}\,a_2=\boxed{0.506\ \text{m}}$$ Beyond ring 3 (cumulative half-width ≈0.86 m from the empty hole) the burn-cut void is ≈1.7 m across – enough clearance to hand off to conventional stoping/production holes for the rest of the 6 m × 4.7 m face, so a 3-ring cut is adequate here.
2. Loading, increasing outward. Ring 1 (smallest burden, closest to the empty hole, greatest risk of choking/cut-off if over-charged): lightest cartridge, 17 mm. Ring 2: 25-32 mm. Ring 3 (largest burden, needs the most energy to break out to the growing void): 40-45 mm. All charged holes are 51 mm, fully stemmed at the collar only (no perimeter decoupling needed here – these are production-strength cut holes, not wall-control holes).

Sequence and timing relative to the round. The empty hole is drilled first with nothing loaded; ring 1 fires first of all (into the single free void the empty hole provides), then ring 2 (into the larger void ring 1 leaves), then ring 3 – each ring on its own short-interval delay (typically a few tens of ms apart, e.g. 25–50 ms, using short-period non-electric delays down the cut) so the rock from the previous ring has time to be ejected/relieved before the next, larger-burden ring fires into it. The cut fires first in the whole round (before any stoping/production holes), because every other hole in the face depends on the cut having already created a free face to break toward; the wall (perimeter, part a) holes fire last, after the cut and all production holes, trimming the already-broken face to the final profile.