24-MMP-B2 Rock Fragmentation · May 2016
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
National Exams, 09-Mmp-B2 Rock Fragmentation, May 2016, 3 hours, closed book (one double-sided aid sheet permitted). Question 1 plus four (4) of Questions 2-6 constitute a complete paper; every question (1-6) is answered in full as a complete study resource.
Reference texts: Persson, Holmberg & Lee, Rock Blasting and Explosives Engineering; C.J. Konya & E.J. Walter, Rock Blasting and Overbreak Control (FHWA); ISEE, Blasters' Handbook, 18th ed.; W. Hustrulid, Blasting Principles for Open Pit Mining; SME Mining Engineering Handbook, 3rd ed., Ch. Drilling and Blasting; W.I. Duvall & C.F. Fogelson, USBM RI 5514 (cratering theory).
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.
Given. Mixture: 95% (94% NH4NO3 / 6% CH2) + 5% Al by mass. Atomic weights C:12, H:1, N:14, O:16, Al:27.
Find. The expected detonation products and how the added aluminum shifts them from plain AN/FO.
Approach. Extend the oxygen-balance (OB) method to the metallised system: each carbon/hydrogen atom demands O to form CO₂/H₂O as usual, and each Al atom additionally demands 1.5 O atoms to form Al₂O₃ (aluminum is not itself an oxidiser – it is a fuel that competes with carbon and hydrogen for the AN's oxygen). Mass-weight the three components' balances to see whether enough oxygen exists to fully oxidise everything.
| Quantity | Value |
|---|---|
| OB of plain 94/6 AN/FO | −1.8% |
| OB of Al (as a fuel, per its own mass) | −88.9% |
| OB of the full 95/5 aluminized mix | −6.1% (oxygen-deficient) |
Adding 5% Al to an already near-balanced ANFO pushes the mixture measurably oxygen-deficient, because aluminum consumes AN's oxygen just as effectively as the carbon in the fuel oil does. The expected detonation products are therefore: N₂ (from the AN nitrogen, released as inert gas – this does not compete for oxygen), H₂O (hydrogen is oxidised first, being the strongest reducer present), Al₂O₃ (solid/molten aluminum oxide – the dominant sink for the "extra" oxygen the aluminum demands, and the source of the characteristic bright fireball and enhanced thermal/blast output of aluminized blends), and, because the −6.1% deficit means not quite enough oxygen remains to finish oxidising the carbon, a mix of CO₂ and some CO (incomplete combustion) rather than CO₂ alone. Some unreacted/partially-oxidised aluminum and soot can also survive if mixing or confinement is imperfect. The net effect of the aluminum is a large increase in heat of detonation and bubble energy (valuable for wet, confined or underwater work) at the cost of oxygen balance – a design trade-off a blast engineer must accept or compensate for by trimming the AN/FO ratio slightly leaner.
A bubble (gassed) emulsion is sensitized by microscopic gas bubbles dispersed through the continuous oxidiser-in-fuel matrix; these bubbles are the hot-spot sites that let the shock front initiate and sustain detonation. Increasing the emulsion's density (by using fewer/smaller bubbles, or by hydrostatic/dynamic over-compression in a deep or decked hole) collapses and shrinks those voids, which raises the critical diameter – a denser emulsion needs a larger charge diameter to sustain steady detonation, because there are fewer/weaker hot-spots per unit volume to drive the reaction front outward against radial energy losses. Conversely, lowering density (more/larger bubbles) lowers critical diameter but eventually over-sensitises and desensitises the product if bubble density gets too high (structural collapse under its own weight, or "dead-pressing" once buried under later-loaded product). There is therefore an optimum density band for a given borehole diameter: too dense and the charge may fail to propagate (critical diameter exceeds hole diameter); too light and detonation pressure/VOD (and hence energy delivered to the rock) is sacrificed.
(1) Dynamic (dead-press) compaction: a shock wave from an adjacent detonation (a nearby hole, or an earlier deck in the same hole) compresses and collapses the sensitizing microballoons/gas bubbles of an emulsion (or the porous AN prills of ANFO) ahead of the reaction front, raising the product's bulk density above its critical density and destroying the hot-spot population needed to sustain detonation – the explosive survives physically intact but can no longer propagate. (2) Channel effect / shock desensitization across an air gap: a shock transmitted through an air gap, stemming plug or rock bridge ahead of the actual detonation front can pre-compress and desensitize the explosive it reaches before the true detonation wave arrives, so that when the front does arrive it meets already-deadened product and low-orders or fails locally – this is the classic mechanism behind sympathetic "cut-offs" between closely-timed adjacent charges.
A strong shock wave from a nearby detonation can prematurely fire an as-yet-undetonated delay detonator by shock-initiating its base charge directly (bypassing the intended pyrotechnic delay element), producing an out-of-sequence ("cut-off") detonation that disrupts the designed timing – this both degrades fragmentation/throw (rows fire before adequate relief exists) and is a serious safety hazard if it advances a hole's firing time unpredictably. Shock can also physically sever a shock-tube/detonating-cord downline before its intended firing instant, causing a misfire instead. Adequate hole-to-hole delay and burden design (so each charge's own shock has attenuated to a safe level before reaching the next undetonated hole), and detonator designs with shock-resistant bases, are the standard mitigations.
An air-deck (an intentional void, top or bottom, left uncharged between the explosive column and the stemming or hole bottom) spreads the same total explosive energy release over a longer effective charge length and delays/attenuates peak borehole pressure, redistributing energy more evenly along the hole and reducing localized crushing near the charge while still generating adequate strain to fracture the rock over the whole column length. For wall control this lets a lower, more uniform pressure pulse act along a perimeter hole, reducing overbreak and vibration relative to a fully coupled charge of the same total mass. For collar fracturing, a small air-gap or reduced charge left immediately below the stemming softens the abrupt pressure step at the collar, reducing the tendency for gas venting/cratering and stemming ejection at the top of the hole while still contributing enough energy to break the collar rock (avoiding a "boot"/toe-like unbroken cap at the surface). The controlling design aspects are the air-deck length and its position (top vs. mid-column vs. bottom), stemming length and material, and the resulting pressure–time history at the hole wall (a longer air-deck lowers peak pressure but lengthens its duration) – getting the balance wrong either under-breaks (deck too long, pressure too low) or reverts to conventional coupled-charge overbreak (deck too short to matter).
Advantages: non-contact and safe (photographed from a safe distance or via drone/fixed camera, no need to physically sample a potentially unstable muckpile); fast, near-real-time feedback that lets the blast engineer correlate fragmentation directly back to the pattern/powder factor of the round just fired; produces a full size distribution (not just a mean size) cheaply and repeatably; and scales to very large sample sizes (thousands of particles per image) compared to hand sieving. Disadvantages: systematically under-samples fines (small particles are hidden behind/beneath larger ones, "fines bias/masking"), cannot see below the exposed muckpile surface (a biased, surface-only sample), requires good, consistent lighting/contrast and calibration (scale reference) to avoid mis-sizing, struggles to separate touching/overlapping fragments (segmentation error), and the software's assumed particle-shape model (typically ellipsoidal) introduces systematic error for very angular or platy rock.
(1) Rosin–Rammler distribution, $$R(x)=\exp\!\left[-\left(\frac{x}{X_c}\right)^n\right]$$ (R = fraction retained above size x, Xc = characteristic size, n = uniformity index). Advantage: only two parameters, a very good empirical fit to blasted rock over most of the practical size range, and n has direct physical meaning (blast uniformity); Xc and n can be predicted from blast design via the Kuz–Ram model without sieving. Disadvantage: systematically over-predicts the fines fraction (below roughly 1% of the mean fragment size) – a well-known Kuz–Ram limitation corrected by later models. (2) Swebrec function (Ouchterlony), a three-parameter curve fitted specifically to correct Rosin–Rammler's fines-end weakness. Advantage: matches sieved/image-analysis fragmentation data (including the fines end) noticeably better than Rosin–Rammler across the full size range. Disadvantage: a third parameter (the curve's undulation exponent) with no simple physical/blast-design interpretation, and it is not as universally built into commercial fragmentation-prediction software as Kuz–Ram.
Timing controls vibration primarily by limiting how many holes' vibration waveforms combine constructively at a given monitoring point: firing holes on different, well-separated delays means each hole's ground vibration is treated (and regulated) as its own smaller event rather than summing with its neighbours into one much larger simultaneous charge. The generally accepted threshold below which two detonations are treated as vibration-simultaneous is about 8 ms (USBM RI 8507) – so a 9 ms delay is only marginally above that threshold and is NOT reliably sufficient in all situations. Real production delays scatter around their nominal value (a few percent for electronic detonators, several percent for pyrotechnic non-electric detonators), so a nominal 9 ms interval can easily overlap into the sub-8 ms simultaneous-summation window purely from normal delay-scatter, especially as more holes/decks accumulate scatter across a large round. A design delay with real margin above 8 ms (commonly 17–25 ms or more, depending on detonator accuracy class) is the safer practice; 9 ms should only be used with high-precision electronic detonators whose scatter is tightly bounded well below the 1 ms margin it leaves.
Ground vibration frequency matters because structural damage potential is governed by the interaction between the ground-motion frequency and a structure's own natural frequency, not by peak particle velocity (PPV) alone. Residential structures typically have natural frequencies in the 4–12 Hz range (walls, floors); a blast vibration whose dominant frequency is close to that range can resonate and amplify the structural response well beyond what the same PPV at a much higher or lower frequency would produce. This is why regulatory vibration limits (e.g. the USBM RI 8507 / OSMRE frequency- dependent PPV limit curves) permit HIGHER PPV at higher dominant frequencies (above roughly 30–40 Hz, where resonant amplification of typical structures is much less likely) and impose the tightest PPV limits in the low-frequency band closest to typical building resonance. Dominant frequency itself is controlled mainly by charge weight per delay, distance and local geology (attenuation path), so blast design (decking, delay selection) can be used to shift the dominant frequency away from the sensitive band as well as to reduce raw PPV.
Air overpressure is dominated by the charge mass detonating per delay (scaled-distance attenuation, Section 2(b) below) and by gas venting at the collar; timing controls it the same way it controls ground vibration – by keeping the number of holes/decks that fire effectively simultaneously (within roughly the same ≈8 ms window) as small as possible, so no single delay's overpressure pulse sums with its neighbours. An appropriate delay is one comfortably above the simultaneity threshold with margin for scatter – typically 17 ms or more between adjacent holes/decks for standard pyrotechnic detonators, with sequencing chosen so the loudest few holes of the round (largest charge per delay, closest to sensitive receptors) are never on the same or an adjacent (sub-8 ms effective) delay number.
Back break (fracturing extending behind the last row of holes into the remaining bench) is driven by: excessive burden or an under-designed last row (the back row sees no free face behind it, so radial cracking and gas pressure extend uncontrolled into the standing bench); insufficient or poor-quality stemming on the back row; excessive powder factor / over-charged back-row holes; inadequate back-row-to-crest setback or timing (firing the back row too early relative to relief development from the rows in front of it); existing structural weaknesses (joints, bedding) running parallel to or behind the back row that channel cracking; and hole deviation on the back row reducing effective burden locally. A trim/ buffer row with a reduced charge (Question 5) is the standard mitigation.
Collaring accuracy and rig set-up/levelling; drill-string/rod stiffness relative to hole depth (long, slender strings flex and "walk"); ground structure – bedding, joints and alternating hard/soft bands deflecting the bit toward the path of least resistance; bit type, size and wear condition; the presence/absence of stabilisers or guide rods; operator skill; and hole angle (inclined holes deviate more readily under gravity/side-load than vertical holes).
Nitrogen oxide fumes form principally when the blast reaction is oxygen-rich (positive OB) – excess free oxygen reacts with the AN's nitrogen to form NO/NO₂ instead of the nitrogen staying inert as N₂. Beyond bulk oxygen balance, the same incomplete/off-design reaction conditions that were flagged in part (a) also promote NOx: water contamination of AN-based product (wet or saturated holes desensitise the mix and drive incomplete, lower-temperature reaction that favours NOx over N₂); poor mixing/segregation of AN and fuel leaving locally oxygen-rich pockets even when the bulk ratio is on-spec; sub-critical diameter or poor confinement (low, unstable VOD reactions do not go to full thermodynamic completion); cold explosive/rock temperature slowing reaction kinetics; ANFO with too little fuel oil (a formulation error pushing OB positive, the opposite extreme from this question's own aluminized, oxygen-deficient blend); and excess or "wet" AN prill residue left in the hole from a previous misfire or spillage, which decomposes with a strongly positive local oxygen balance. Good mixing quality control, correct AN/fuel ratio, dry holes and adequate confinement/priming are the standard controls.
