Question

In a bench blasting, as shown, 49 kg of explosive is put in each hole. The detonation time of holes, in millisecond, and the associated scale distance (SD) vs. peak particle velocity (PPV) plot for the given blast pattern is shown.

The PPV at a distance of 100 m, in \( \text{mm}\,\text{s}^{-1} \), is . (rounded off to two decimal places)

Hint:

Find the largest charge weight that detonates in the same delay from the firing time diagram, use it to scale the distance, then plug into the given PPV versus scaled distance equation.

Answer 1

Correct Answer: 7.79

Step 1: Understanding the Concept:
In production blasting, holes are not all fired at once, they are fired in a timed sequence (millisecond delays) so that each hole breaks toward a free face created by the hole before it. Vibration at a distant point depends only on the charge that fires at any one instant, not on the total charge in the whole blast, because delayed charges act as separate, smaller events.

Step 2: Key Formula or Approach:
The scaled distance approach used by USBM style vibration laws is $SD = D/\sqrt{W}$, where $W$ is the biggest single-instant (per delay) charge weight, and $D$ is the distance to the point of interest. The site specific attenuation curve then gives $PPV = 250(SD)^{-1.5}$.

Step 3: Detailed Explanation:
From the timing diagram, the front row holes fire at 0, 25, 50 and 75 ms, and the back row holes fire at 50, 75 and 100 ms. Two delay times, 50 ms and 75 ms, are shared between a front row hole and a back row hole, meaning a pair of holes goes off together at each of those instants.
Since every hole carries 49 kg, the charge firing simultaneously at these shared instants is $W = 49 + 49 = 98\ kg$, and this is larger than any single hole's 49 kg, so it is the value that controls vibration.
The scaled distance at 100 m is $SD = 100/\sqrt{98} = 100/9.8995 = 10.10\ m\,kg^{-0.5}$.
Raising this to the power 1.5 gives $10.10^{1.5} = 32.11$, so $PPV = 250/32.11 = 7.79\ mm/s$.

Step 4: Final Answer:
Because a pair of holes coincides at 50 ms and again at 75 ms, the governing per delay charge is 98 kg, giving a predicted PPV of about 7.79 mm/s at 100 m.