Geomechanics & Ground Control

Ground Vibrations

Scaled distance and the peak particle velocity (PPV) prediction that keeps blast vibrations within safe limits.

PART 1

Topic Breakdown & Traps

The Engineering Principle

Blasting radiates ground vibrations whose severity is judged by the peak particle velocity (PPV). Field data collapse onto a single curve when plotted against the scaled distance — the distance

D

divided by the square root of the maximum charge per delay

W

. The USBM-type prediction is

P P V = k (D / W)^{- β}

. Re-arranged, it sets the maximum charge per delay that keeps PPV below a damage threshold at a given distance.

The Core Formula Matrix

Scaled distance:

S D = \frac{D}{W}

(

D

= distance,

W

= charge per delay).

PPV prediction:

P P V = k (S D)^{- β} = k (\frac{D}{W})^{- β}

.

Max charge per delay for an allowable

S D

W = (\frac{D}{S D})^{2}

The ‘IIT Traps’

⚠
**Square-root scaling: $W$ , not $W$ .** Charge-weight enters under a square root for cylindrical charges.
⚠
Larger scaled distance ⇒ lower PPV. The exponent is negative; bigger $S D$ is safer.
⚠
** $W$ is charge *per delay*, not the total round.** Delays are precisely what keep $W$ (and PPV) down.

PART 2

Progressive 3-Tier Question Suite

Q1BASIC1 Mark · MCQ

A blast uses

25 kg

per delay and is recorded

100 m

away. The scaled distance is:

Q2MEDIUM2 Marks · NAT

Using

P P V = 1140 (S D)^{- 1.6}

with

S D = 20

, the predicted peak particle velocity is ______ mm/s. (Round off to two decimal places.)

mm/s

Q3HARD2 Marks · NAT

To keep the scaled distance at

25 m/\sqrtkg

for a structure

50 m

away, the maximum charge per delay is ______ kg. (Round off to two decimal places.)