Question 7 of 7: Underground Cut Design and Final-Wall Trim Blasting

Question 7: Underground Cut Design and Final-Wall Trim Blasting (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) Parallel-hole (burn) cut design – 5 m × 4 m tunnel

Approach. With only one empty (uncharged) relief hole available (76 mm), a classical expanding-square parallel/burn cut is used: charged 50 mm holes are arranged in successively larger square rings around the empty hole, each ring breaking into the void created by the previous one, so the burden each ring's charge must move roughly doubles ring-to-ring. A commonly used first-ring burden for a single empty hole is b₁ ≈ 1.5×the empty-hole diameter (tight enough that the charge reliably breaks and relieves into the hole rather than just cratering around it).

1. Section 1 (4 holes). b₁ = 1.5×76 mm ≈ 0.114 m from the empty-hole centre – the tightest ring, breaking directly into the 76 mm void.
2. Section 2 (4 holes). b₂ ≈ 2×b₁ ≈ 0.23 m, breaking into the (now much larger) Section-1 void.
3. Section 3 (4 holes). b₃ ≈ 3.4×b₁ ≈ 0.39 m.
4. Section 4 (enlargement, 4 holes). b₄ ≈ 5.6×b₁ ≈ 0.64 m, growing the cut opening to roughly 1.2–1.3 m square – a sufficient free-face opening for the remaining stoping (relief) and perimeter holes to break to.
5. Remaining round. Stoping/relief holes at a standard tunnel burden/spacing (≈0.9–1.0 m for 50 mm charge holes in this rock class) break the bulk of the 5×4 m face outward from the enlarged cut opening; perimeter/contour holes (smooth blasting, light decoupled charge – see part b) trim the final profile; floor lifter holes (angled slightly downward/outward) are loaded heaviest to throw the muck clear.

Initiation sequence and delays. The empty hole is never charged. Sections fire strictly centre-out on increasing delay numbers so each ring always breaks into an already-open void: Section 1 on the earliest delay (e.g. #1, ≈0–25 ms), Section 2 next (≈25–50 ms), Section 3 (≈75–100 ms), Section 4/enlargement (≈100–150 ms); the stoping/relief holes follow on progressively later delays working outward from the enlarged cut toward the walls and back (≈175–300 ms); perimeter/contour holes fire on a late, closely-spaced delay group (lightly charged, smooth blasting) to trim the profile without over-breaking the already-relieved rock behind them; and the floor lifters fire last (≈350–400 ms +) so the entire face has already been broken and can be thrown forward and out of the round's own muckpile. Short delay-interval spacing (25 ms typical) between successive sections is used throughout to keep each ring's rock movement well separated from the next, minimising choke/cut-off risk between closely spaced cut holes.

(b) Underground final-wall (smooth) blast – 160 MPa, 50 mm holes

Given. Hole diameter D_h=50 mm, length 5 m; UCS=160 MPa, tensile strength σ_t=5 MPa; emulsion available at 25/32/40/50 mm, ρ=1.15 g/cm³, VOD=5500 m/s.

Find. Hole spacing and charge/loading for a smooth (perimeter-control) final-wall blast.

Approach. Smooth blasting works by keeping the borehole wall pressure well below the rock's crushing strength while still exceeding its tensile strength enough to propagate a clean radial fracture between adjacent holes; this is achieved with a decoupled (small cartridge in the 50 mm hole) charge, run the full hole length, at close spacing.

1. Select maximum decoupling: 25 mm cartridge in the 50 mm hole. Decoupling ratio d_c/d_h = 25/50 = 0.5 (the smallest cartridge offered gives the softest, most controllable loading – the correct choice for final-wall control).
2. Detonation pressure of the emulsion (fully coupled reference). $$P_d=\frac{\rho_e\,VOD^2}{4}=\frac{1.15\times5.5^2}{4}=8.70\ \text{GPa}$$
3. Decoupled borehole wall pressure (adiabatic gas-expansion approximation, P_b=P_d(d_c/d_h)^2.4): $$P_b=8.70\times(0.5)^{2.4}=8.70\times0.190=\boxed{1.65\ \text{GPa}\ (1648\ \text{MPa})}$$ – still well above the 160 MPa UCS (some crushing right at the borehole wall is normal and acceptable in smooth blasting), but reduced roughly 5-fold from the fully-coupled detonation pressure, which is what protects the rock behind the final-wall line from the fracture-inducing overpressure a fully coupled charge would deliver.
4. Linear charge concentration of the 25 mm string. $$q_L=\frac{\pi}{4}(0.025)^2\times1150=0.565\ \text{kg/m}$$ – on the higher side of typical smooth-blasting guideline concentrations (≈0.15–0.5 kg/m for this hole-diameter class), so the design uses a spaced (decked) string, not a solid column, to bring the effective average down (see loading note below).
5. Perimeter hole spacing. Standard smooth-blasting guideline S≈10–12×D_h: $$S=12\times0.050=\boxed{0.60\ \text{m}}$$

Loading. Run the 25 mm emulsion cartridges the full 5 m length but spaced (short air gaps between cartridges, taped to a detonating-cord downline) rather than butted solid, targeting roughly 60% coverage to bring the effective average linear concentration down to ≈0.34 kg/m, close to published smooth-blasting targets for this hole size; centre the string in the 50 mm hole (radial air-decoupling on all sides) with light stemming (drill cuttings or fine sand) at the collar only. Fire the perimeter/contour row on its own, latest delay group (after the buffer and main-round holes have already relieved) so the trim blast works against an already-open face rather than a confined one.

(c) Open-pit final-wall (trim) blast – vertical 102 mm holes, ANFO

Given. Vertical holes, D_h=102 mm, length 12 m; ANFO ρ=0.85 g/cm³ (only explosive specified – no rock strength given for this sub-part).

Find. Hole spacing and loading for the open-pit final wall.

Approach. ANFO cannot be radially decoupled like a cartridge product, so wall control is achieved instead through a tight trim-row spacing and a reduced, air-decked (spaced) charge column rather than a full continuous column, following the same smooth-blasting principle as part (b) applied to a bulk-loaded product.

1. Fully-coupled linear charge concentration (reference, if loaded solid). $$q_{L,full}=\frac{\pi}{4}(0.102)^2\times850=6.95\ \text{kg/m}$$ – this is production-blast energy, far too high for a controlled final wall.
2. Trim-row spacing (same S≈12×D_h guideline as part b): $$S=12\times0.102=\boxed{1.22\ \text{m}}$$
3. Air-decked loading to cut the effective linear concentration. Load alternating ≈1 m charged sections separated by ≈1 m stemmed air-deck gaps along the column, halving the effective average concentration to ≈3.5 kg/m – still a substantial reduction from the fully coupled value, applied with light collar stemming (≈1.0–1.2 m) and, if available, a reduced-density (aerated) ANFO to soften the charge further.