Drilling & BlastingFREE· Reviewed Jun 2026

Drilling & Blasting

Bench-blast geometry (burden, spacing, subgrade, stemming), powder factor, linear charge concentration and detonation pressure — the most arithmetic-heavy cluster in the paper.

Section 1

Recent Trend Analysis (2017–2026)

Drilling & Blasting reliably carries 4–6 marks and is the section where a clean unit discipline wins or loses the most marks per minute.

The decade-long shift in question style:
- 2017–2019 — property recall: rank explosives by VOD, define powder factor, state the role of stemming and subgrade drilling. Mostly 1-mark MCQs.
- 2020–2022 — single-step computation: a powder factor from a given charge and volume, or a detonation pressure from density and VOD.
- 2023–2026 — full multi-variable NAT chains: hole length → charge length → linear charge concentration → charge per hole → powder factor, and complete bench-geometry design with subgrade and stemming proportioned to the burden.

Exact recurring themes you must own:
- Charge per hole via the linear concentration

l = \frac{π}{4} d^{2} ρ_{e}

over the charged length.
- Powder factor in both

k g / m^{3}

and

k g / t o nn e

(the density conversion trap).
- Detonation pressure

P_{d} = ρ_{e} V_{O D}^{2} /4

and the borehole-pressure ≈ half rule.
- Bench proportions:

S = 1.0 - 1.4 B

, subgrade

J \approx 0.3 B

, stemming

T \approx 0.7 B

.
- A rising count of MSQs on which blast-design / explosive-selection statements are simultaneously valid — one wrong tick zeroes the mark.

Section 2

Master Formula Matrix & Derivations

Powder Factor (Specific Charge)

The mass of explosive consumed per unit volume (or mass) of rock broken — the headline efficiency metric of any blast.

q = \frac{W _{e x p}}{V _{r oc k}} (k g / m^{3}), q_{t} = \frac{W _{e x p}}{ρ _{r} V _{r oc k}} (k g / t o nn e)

⚡ Exam shortcut ·

Convert between the two with the rock density:

q_{t} = q / ρ_{r}

(with

ρ_{r}

t / m^{3}

). Typical surface bench blasting:

q \approx 0.3 - 0.8 k g / m^{3}

Variable Index (SI units)

Symbol	Meaning	SI unit
$q$	Powder factor (volumetric)	$k g / m^{3}$
$q_{t}$	Powder factor (gravimetric)	$k g / t o nn e$
$W_{e x p}$	Explosive mass per blast (or per hole)	$k g$
$V_{r oc k}$	Rock volume broken	$m^{3}$
$ρ_{r}$	Rock density	$t / m^{3}$ (or $k g / m^{3}$ )

Bench Geometry (Burden, Spacing, Subgrade, Stemming)

Sound blast design proportions every length to the burden — the distance from the charge to the nearest free face.

B = k_{b} d, S = k_{s} B, J = 0.3 B, T = 0.7 B, L = H + J

⚡ Exam shortcut ·

Practical ranges:

k_{b} \approx 25 - 40

(hole diameters),

k_{s} \approx 1.0 - 1.4

. Burden

B

is perpendicular to the face; spacing

S

is along the row — never swap them in

V = B S H

Variable Index (SI units)

Symbol	Meaning	SI unit
$B$	Burden (charge-to-free-face distance)	$m$
$S$	Spacing between holes in a row	$m$
$d$	Blasthole diameter	$m$ (convert from $mm$ )
$J$	Subgrade (subdrill) depth	$m$
$T$	Stemming length	$m$
$H$	Bench height	$m$
$L$	Total hole length ( $H + J$ )	$m$

Linear Charge Concentration & Charge per Hole

A column charge filling the hole bore carries a fixed mass per metre; the hole charge is that concentration over the charged length only.

l = \frac{π}{4} d^{2} ρ_{e}, W_{h} = l (L - T)

⚡ Exam shortcut ·

Charged length

= L - T

(the stemming carries no explosive). Keep

d

in metres and

ρ_{e}

k g / m^{3}

l

is in

k g / m

directly.

Variable Index (SI units)

Symbol	Meaning	SI unit
$l$	Linear charge concentration	$k g / m$
$d$	Blasthole diameter	$m$
$ρ_{e}$	Explosive density	$k g / m^{3}$
$W_{h}$	Charge per hole	$k g$
$(L - T)$	Charged (column) length	$m$

Volume / Tonnage Broken & Number of Holes

Each production hole breaks the rock prism defined by its burden, spacing and the bench height (not the hole length).

V_{h} = B S H, N = \frac{V _{t o t a l}}{B S H}, q = \frac{W _{h}}{B S H}

⚡ Exam shortcut ·

Use **bench height

H

**, not hole length

L

, for the broken volume — the subgrade only ensures a clean floor, it does not add to the prism.

Variable Index (SI units)

Symbol	Meaning	SI unit
$V_{h}$	Rock volume broken per hole	$m^{3}$
$N$	Number of holes for the round	count
$q$	Powder factor	$k g / m^{3}$

Detonation & Borehole Pressure

The detonation pressure at the reaction front scales with explosive density and the square of the detonation velocity.

P_{d} = \frac{ρ _{e} V _{O D}^{2}}{4}, P_{b} \approx \frac{1}{2} P_{d}

⚡ Exam shortcut ·

With

ρ_{e}

k g / m^{3}

and

V_{O D}

m / s

P_{d}

comes out in

P a

— divide by

1 0^{9}

for GPa. The coupled borehole pressure

P_{b}

is roughly half the detonation pressure.

Variable Index (SI units)

Symbol	Meaning	SI unit
$P_{d}$	Detonation pressure	$P a$ (≈ GPa range)
$P_{b}$	Borehole (blasthole) pressure	$P a$
$ρ_{e}$	Explosive density	$k g / m^{3}$
$V_{O D}$	Velocity of detonation	$m / s$

Section 3

The "IIT Trap" Warning System

Burden ↔ spacing swap. $B$ (perpendicular to the face) and $S$ (along the row) are distinct; both appear in $V = B S H$ , so swapping them changes the geometry ratio and the powder factor. The setters offer the swapped-value distractor every time.
**Diameter unit ( $mm$ vs $m$ ).** Hole diameter is quoted in $mm$ but the charge concentration needs $d$ in metres. A $100 mm$ hole is $0.1 m$ ; forgetting the conversion scales $l$ by $1 0^{6}$ .
Detonation-pressure constant. $P_{d} = ρ_{e} V_{O D}^{2} /4$ . The borehole pressure uses roughly $/8$ (half of $P_{d}$ ) — picking the wrong divisor (4 vs 8) is the classic NAT trap.
Powder factor units. $k g / m^{3}$ and $k g / t o nn e$ differ by the rock density $ρ_{r}$ . Reporting $k g / m^{3}$ when the question asks $k g / t o nn e$ (or vice-versa) is a seeded wrong option.
Subgrade does NOT add to broken volume. The prism uses bench height $H$ ; only the hole length $L = H + J$ uses the subgrade. Using $L$ in $V = B S L$ over-estimates tonnage.
Stemming carries no charge. Charged length is $L - T$ , not $L$ . Charging the full hole length inflates $W_{h}$ and the powder factor.
**Radius vs diameter in $\frac{π}{4} d^{2}$ . The bore area uses diameter**; slipping in the radius understates the charge concentration four-fold.
VOD is squared. Detonation pressure $\propto V_{O D}^{2}$ — doubling VOD quadruples $P_{d}$ . The linear distractor ('pressure also doubles') is always present.

Section 4

High-Fidelity Core Examples

Example 12-mark complexity

A surface bench is blasted with vertical holes of diameter

d = 100 mm

. Bench height

H = 10 m

, burden

B = 3 m

, spacing

S = 3.5 m

, subgrade drilling

J = 0.9 m

and stemming

T = 2.5 m

. The explosive (column charge) has density

ρ_{e} = 1200 k g / m^{3}

. Determine the charge per hole and the powder factor in

k g / m^{3}

Given Parameters Matrix (clean SI)

Hole diameter ( $d$ )	$100 mm = 0.10 m$
Bench height ( $H$ )	$10 m$
Burden ( $B$ )	$3 m$
Spacing ( $S$ )	$3.5 m$
Subgrade ( $J$ )	$0.9 m$
Stemming ( $T$ )	$2.5 m$
Explosive density ( $ρ_{e}$ )	$1200 k g / m^{3}$

Algebraic Derivation Track

Step 1 — Hole length and charged length:

L = H + J = 10 + 0.9 = 10.9 m, L - T = 10.9 - 2.5 = 8.4 m

Step 2 — Linear charge concentration:

l = \frac{π}{4} d^{2} ρ_{e} = 0.7854 \times (0.10)^{2} \times 1200 = 0.7854 \times 0.01 \times 1200 = 9.4248 k g / m

Step 3 — Charge per hole:

W_{h} = l (L - T) = 9.4248 \times 8.4 = 79.17 k g

Step 4 — Volume broken per hole (bench height, NOT hole length):

V_{h} = B S H = 3 \times 3.5 \times 10 = 105 m^{3}

Step 5 — Powder factor:

q = \frac{W _{h}}{V _{h}} = \frac{79.17}{105} = 0.754 k g / m^{3}

🎯 Final target & accepted range ·

Charge per hole

W_{h} \approx 79.2 kg

(accept

78 - 80 kg

); powder factor

q \approx 0.75 kg/ m^{3}

(accept

0.74 - 0.77

) — a typical, well-designed surface round.

Example 22-mark complexity

ANFO of density

ρ_{e} = 850 k g / m^{3}

detonates at a velocity

V_{O D} = 4000 m / s

. Estimate its detonation pressure and the approximate borehole pressure.

Given Parameters Matrix (clean SI)

Explosive density ( $ρ_{e}$ )	$850 k g / m^{3}$
Detonation velocity ( $V_{O D}$ )	$4000 m / s$

Algebraic Derivation Track

Step 1 — Detonation pressure:

P_{d} = \frac{ρ _{e} V _{O D}^{2}}{4} = \frac{850 \times ( 4000 ) ^{2}}{4} = \frac{850 \times 1.6 \times 1 0 ^{7}}{4}

P_{d} = \frac{1.36 \times 1 0 ^{10}}{4} = 3.4 \times 1 0^{9} P a = 3.4 GP a

Step 2 — Borehole pressure (≈ half of detonation pressure):

P_{b} \approx \frac{1}{2} P_{d} = \frac{1}{2} (3.4) = 1.7 GP a

🎯 Final target & accepted range ·

Detonation pressure

P_{d} \approx 3.4 GPa

(

3400 M P a

, accept

3.3 - 3.5 GPa

); borehole pressure

P_{b} \approx 1.7 GPa

. Note the square law on VOD — a 25% faster explosive raises

P_{d}

by ~56%.