Scaled distance, the number behind vibration limits

Ground vibration from a blast falls off with distance and rises with the amount of explosive detonating at the same time. Instead of tracking two numbers, blasting practice combines them into one: the scaled distance, which is the distance divided by the square root of the charge per delay (R ÷ √W). A blast 300 m away firing 120 kg per delay has a scaled distance of about 27 m/√kg. So does a blast 150 m away firing 30 kg per delay, and the two tend to produce a similar peak particle velocity in the same ground.

It is not the total in the shot. It is the largest mass of explosive detonating within a short window, usually taken as 8 milliseconds, because charges closer together than that reinforce each other as if they were one. Deck charges on separate delays, and electronic timing, are the tools for bringing it down without taking explosive out of the ground.

The estimate uses PPV = K × (scaled distance)^−β. K sets the level and β sets how fast vibration falls with scaled distance. They belong to the ground between the blast and the monitor, and to how the site blasts. The way to find them is to monitor a run of blasts, plot peak particle velocity against scaled distance on log axes, and fit a line. Standards quote generic values as a starting point for sites with no data. Those values are not a property of your site, and a regression from a dozen monitored blasts will usually replace them with something quite different.

Planning. Given a limit at a structure and a distance, the equation turns around to give the largest charge per delay that should meet the limit. That lets a design be checked before it is drilled, and lets a shot near a sensitive receiver be decked or re-timed in advance. Compliance is still decided by the monitor on the day and by the conditions of the approval.

Close in, where scaled distances are small, the law is least reliable. It is also silent on airblast, which has its own scaling and its own limits, and on the direction of the structure from the blast. A single regression covers one path through one ground; a site with a different ground on one side will need a different fit for that side.