Question 2 of 6: Iron-Ore Powder-Factor Design and Pattern Tie-Ins

Question 2: Iron-Ore Powder-Factor Design and Pattern Tie-Ins (21 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) Powder factor for 80% passing < 60 cm

Given.

Find. The powder factor (specific charge) K that limits the Kuznetsov mean fragment size to the 60 cm target.

Approach. Rate the rock via Lilly's Blastability Index (UCS and E are both given specifically to feed this), fix the per-hole charge mass from the given hole geometry (diameter, subdrill, collar – independent of burden/spacing), then invert the Kuz–Ram mean-fragmentation-size equation for the powder factor K that drives X to the 60 cm target. K is a single ratio (charge mass / rock volume per hole) so it can be solved directly without needing burden and spacing individually.

1. Charge mass per hole (fixed by geometry, not by K). Total hole depth = H + subdrill = 12 + 1 = 13 m; charge (column) length = 13 − 4.6 = 8.4 m; hole area = $$\frac{\pi}{4}(0.406)^2=0.1295\ \text{m}^2$$ $$Q=8.4\times0.1295\times1320=\boxed{1435\ \text{kg per hole}}$$
2. Rock factor A (Lilly's Blastability Index). Massive rock with no joint data given → RMD = 50, RDI = 50 (both at their competent-rock ceiling); UCS > 50 MPa → hardness factor HF = E(GPa)/3 = 110/3 = 36.7: $$A=0.06(RMD+RDI+HF)=0.06(50+50+36.7)=\boxed{8.2}$$
3. Explosive-strength correction. Kuznetsov's equation is calibrated to ANFO (RWS = 100); the standard correction for a different explosive is $$\left(\frac{115}{RWS}\right)^{19/30}=\left(\frac{115}{92}\right)^{0.633}=1.152$$
4. Invert Kuznetsov for K. Kuznetsov's mean-fragment-size equation (X in cm, V/Q in m³/kg, Q in kg) with K = Q/V (kg/m³, the powder factor): $$X=A\,K^{-0.8}Q^{1/6}\left(\frac{115}{RWS}\right)^{19/30}$$ $$Q^{1/6}=1435^{1/6}=3.36,\qquad A\cdot Q^{1/6}\cdot 1.152=8.2\times3.36\times1.152=31.7$$ Setting X = 60 cm and solving for K: $$60=31.7\,K^{-0.8}\ \Rightarrow\ K^{-0.8}=1.891\ \Rightarrow\ K=1.891^{-1/0.8}=\boxed{0.45\ \text{kg/m}^3}$$

A powder factor of about 0.45 kg/m³ is a realistic value for a massive, hard (UCS 300 MPa) iron ore at this scale of blast – consistent with the rock being harder than average (A = 8.2, above the A≈7 baseline for average blastability), which is why a moderately higher-than-typical powder factor is needed to still hit a fine 60 cm target. Any combination of burden and spacing satisfying B×S = Q/(K×H) = 1435/(0.45×12) ≈ 266 m² per hole (e.g. B≈14.5 m, S≈18.3 m at the standard S/B≈1.26 ratio for a staggered pattern) delivers this powder factor for the given 406 mm hole geometry.

(b) Tie-ins and delays for the Figure 1 pattern

Figure 1 shows a large multi-row pattern (roughly five rows by eighteen holes, staggered) free-faced along the top row shown in the figure. The governing tie-in principle is to fire each hole into the maximum relief created by the holes that fired immediately before it, while keeping the instantaneous charge per delay to a single hole (or single deck) so vibration and airblast are controlled per Q1(j)/(h). Recommended design:

1. Initiation point and direction. Initiate from one corner of the pattern closest to the existing free face, so the blast can retreat diagonally across the full pattern – this gives every hole in every subsequent row a genuine, growing free face rather than firing rows simultaneously into an unrelieved bench.
2. V1 (diagonal echelon) tie-in. Use surface trunklines connecting each hole to the next along diagonal lines (a "V1" pattern): hole-to-hole delay along the diagonal of 17–25 ms (comfortably above the ≈8 ms vibration/airblast simultaneity threshold, Q1(h)/(j)), with each successive diagonal row offset by one delay increment from its neighbour so the blast sweeps outward from the initiation corner in a widening V.
3. Row-to-row lag. Ensure the last hole of a given diagonal fires with enough time lag relative to the first hole of the next diagonal (typically 25–42 ms row-to-row) for burden relief/face movement to develop, avoiding the "coarse fragmentation / high vibration" failure mode of firing an unrelieved row.
4. Throw control. Angle the diagonal lines so muck is thrown toward the pattern's open/low side (away from haul roads or other infrastructure implied by the plan view), and keep the corner-most (least confined) holes on a slightly longer delay so they do not lead the round and throw material uncontrolled ahead of the main muckpile.