Question 4 of 7: Fragmentation, Uniformity, Flyrock and Final-Wall Blast Design

Question 4: Fragmentation, Uniformity, Flyrock and Final-Wall Blast Design (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 controlling average fragment size

Powder factor (kg explosive per m³ rock) – higher powder factor gives finer fragmentation (Kuznetsov: X₀₁&sub2; ∝ K^-0.8); burden and spacing – a burden too large for the charge relieves poorly and coarsens the result, one too small over-confines and produces excess fines; borehole diameter – larger diameter concentrates the same powder factor into fewer, more widely spaced charges, coarsening the mean size for a fixed K; explosive type/energy (VOD, density, weight strength) – higher-energy product breaks rock finer at the same charge mass; rock mass structure (joint spacing, bedding, in-situ block size) – naturally blocky rock fragments along its own discontinuities and can be either finer or coarser than a massive rock at the same K; delay timing between holes/rows – adequate delay lets each row relieve into the previous void, improving breakage; too little delay causes charges to compete.

(b) Parameters controlling fragmentation uniformity

Pattern regularity (consistent burden/spacing, drilling accuracy) – deviated holes create local over- and under-charged zones that widen the size distribution; uniformity of the rock mass itself (joint spacing variability across the blast) – a rock mass with widely varying in-situ block size cannot fragment uniformly regardless of design; charge distribution along the hole (deck vs. continuous column, stemming length) – a well-distributed column breaks the whole burden height evenly, a short or poorly placed charge leaves a coarse toe/collar zone; timing scatter between detonators – large delay scatter causes some charges to act almost simultaneously (locally coarser or overbroken) and others in isolation; and explosive energy uniformity along the column (consistent density/VOD, no dead-pressed sections).

(c) Blast parameters controlling flyrock travel

Stemming length and quality – inadequate or poorly-sized stemming (wrong aggregate, too short) vents high-pressure gas early and is the single most common flyrock cause; burden – a burden that is too small for the charge (or locally reduced by drilling error/mapping error) lets face-burst gas propel rock far beyond the design throw; powder factor/charge concentration – excess explosive energy for the confining rock mass increases both throw velocity and distance; structural weaknesses (joints, mud seams, voids) that vent gas along an unpredicted path; and initiation timing – charges that fire before the preceding row has adequately relieved add confinement-driven overpressure that increases flyrock risk.

(d) Collar for the 165 mm holes

Given. De₁ = 102 mm, collar/stemming T₁ = 2.0 m (no flyrock issues at this ratio); new diameter De₂ = 165 mm.

Find. Recommended stemming (collar) length T₂.

Approach. Stemming confinement scales with borehole diameter (the classic rule of thumb is T ≈ 20–30×De to hold enough inert plug mass over the charge to resist gas ejection); since the existing 102 mm design already runs a well-proven, flyrock-free ratio, scale the collar proportionally to the new diameter to preserve that same ratio.

1. Existing stemming ratio. $$\frac{T_1}{De_1}=\frac{2.0\,\text{m}}{0.102\,\text{m}}=19.6$$ – sits right in the standard 20×De confinement guideline (Konya).
2. Scale to the new diameter, holding the ratio constant. $$T_2=T_1\times\frac{De_2}{De_1}=2.0\times\frac{165}{102}=\boxed{3.24\ \text{m}}$$

Why this ratio, and implications. Holding T/De constant keeps the same confining rock mass (and hence gas-retention time) over the collar as the diameter grows, so the borehole that was already proven flyrock-free at 102 mm stays so at 165 mm. If the collar were left at the old 2.0 m instead, the ratio would fall to only 2.0/0.165 = 12.1×De – well under the 20×De guideline – and the larger, higher-energy 165 mm charge would very likely vent through an under-stemmed collar, creating a flyrock hazard that did not exist at the smaller diameter. On fragmentation, moving to 165 mm holes (even keeping powder factor constant) concentrates the same explosive energy into fewer, more widely spaced charges – burden and spacing both scale up roughly with diameter – which by the Kuznetsov relationship coarsens the average fragment size (fewer discontinuities of broken rock per unit volume, larger inter-hole spacing between energy sources) even though productivity (m³ drilled per metre of hole) improves. The quarry should expect to trade some fragmentation fineness for drilling/loading productivity unless the powder factor is deliberately increased to compensate – the design approach used in part (e) below.

(e) Blast design for a final-wall approach panel – 200 MPa massive rock

Given. Massive rock, UCS = 200 MPa (assume rock SG ≈ 2.7, typical of a competent, high-strength massive host – check, no rock density given); bench height H = 14 m; candidate diameters 311 mm and 165 mm; target average fragment size X₀₁&sub2; = 25 cm; AN/FO (ρ=0.85 g/cm³) or blend (ρ=1.3 g/cm³, RWS=0.95 rel. ANFO); panel 100 m × 50 m.

Find. Recommended diameter/explosive combination and full pattern (burden B, spacing S, subdrill J, stemming T, hole depth, charge mass, powder factor) that delivers X₀₁&sub2; ≈ 25 cm, plus the resulting hole count and explosive tonnage for the panel.

Approach. (1) Screen the two diameters on stiffness ratio SR = H/B (Konya-type burden B=0.012(2SG_e/SG_r+1.5)De) – SR < 2 gives poor toe breakage/boulders and is rejected outright for a hard, massive rock. (2) For the surviving diameter, apply the Kuznetsov mean-fragment-size equation X₀₁&sub2;=A·(V/Q)^0.8·Q^1/6 (with a rock factor A appropriate to massive, weakly-fissured hard rock) to find the tightened burden that hits the 25 cm target, since the standard Konya burden alone is not tight enough for this competitive strength/target-size combination.

1. Stiffness-ratio screen (ANFO, SG_r=2.7). $$B_{165}=0.012\left(\frac{2(0.85)}{2.7}+1.5\right)(165)=4.22\ \text{m}\;\Rightarrow\;SR=\frac{14}{4.22}=3.32$$ $$B_{311}=0.012\left(\frac{2(0.85)}{2.7}+1.5\right)(311)=7.95\ \text{m}\;\Rightarrow\;SR=\frac{14}{7.95}=1.76$$ 311 mm gives SR < 2 in either explosive – the burden it demands is too large relative to the 14 m bench for good toe breakage/fragmentation control, so 165 mm is selected and 311 mm is rejected regardless of explosive choice.
2. Tighten the 165 mm pattern to hit X₀₁&sub2;=25 cm. Using S=1.15B, J=0.3B, T=0.7B (standard staggered-pattern ratios) and rock factor A=13 (massive, weakly-fissured hard rock, Cunningham/Kuznetsov scale – check, no RQD/joint data given), solving X₀₁&sub2;(B)=25 cm numerically for AN/FO gives $$\boxed{B=3.23\ \text{m},\ S=3.72\ \text{m},\ J=0.97\ \text{m},\ T=2.26\ \text{m}}$$
3. Resulting hole depth, charge and powder factor. Hole depth = H+J = 14.97 m; charge length = 14.97−2.26 = 12.71 m; Area(165mm) = 0.02138 m². $$Q=12.71\times0.02138\times850=230.9\ \text{kg/hole},\quad K=\frac{Q}{B\,S\,H}=\frac{230.9}{3.23\times3.72\times14}=1.37\ \text{kg/m}^3$$ – a realistic powder factor for hard, massive rock (typical range 0.7–1.5 kg/m³).
4. Panel hole count and total explosive (100 m × 50 m). $$n_{row}=\left\lceil\frac{100}{3.72}\right\rceil+1=27,\quad n_{rows}=\left\lceil\frac{50}{3.23}\right\rceil+1=16$$ $$N=27\times16=432\ \text{holes},\qquad \boxed{Total\ AN/FO \approx 432\times230.9\approx99{,}800\ \text{kg}\approx99.8\ \text{t}}$$