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Overcoming Oversize: Oversize and stiffness ratio (Part 2)

By |  July 13, 2021

Pit & Quarry’s “Overcoming Oversize” series discusses the generation of oversize in the blasting process and techniques to reduce or eliminate it. Next month’s article will discuss oversize and confinement, emphasizing how improper spacing leads to oversize through a splitting action, how to identify this and more.  Here’s part two of the four-part series.


Photo: Picsguru/iStock / Getty Images Plus/Getty Images

While a bigger drill diameter may result in some lower upfront costs, it can result in more oversize and worse blast performance. Photo: Picsguru/iStock / Getty Images Plus/Getty Images

Bigger is always better.

This trend has permeated all parts of society, including the mining industry. We’ve seen increases in size and capacity for nearly all equipment, and new challenges have arrived to manage these massive machines.

This really hit home when I was consulting for a large coal mine in northwest Canada. The mine had just unveiled the world’s largest shovel, a massive machine that could move coal and overburden better than any other machine on Earth. The double-spotted haul trucks could barely keep up with this new machine, and the mine was extremely proud to have this flagship shovel at its operation.

The biggest issue now was feeding the shovel with enough material. That meant possibly increasing the drill diameter to allow for larger burdens and spacing, meaning more rock per hole. This larger burden would also mean a lower stiffness ratio – and that would lead to more flyrock and more violence, among other things.

The oversize was not a problem for this site. Its new shovel could pick up more than 135 short tons per pass, and the overburden was a waste product.

While this coal mine did not have to worry about oversize, most sites do not have the luxury of having the world’s largest shovel and moving material that will not be crushed. Instead, oversize is a constant headache to most operations and a significant cost when factoring in secondary breakage. For these operations, bigger is not always better – especially when it comes to drilling.

Stiffness ratio

Photo: Anthony J. Konya

This table illustrate the differences in blast performance based on stiffness ratio. Click to expand.

The term “stiffness ratio” was first used in 1969 by Calvin Konya in his fundamental work on blasthole spacing.

Konya discovered there was a relationship between the bench height, the burden and the spacing of the blasthole. Stiffness ratio was developed as a dimensionless constant to express this relationship between terms.

Further research by Konya indicated that not only did the blasthole spacing change as a result of stiffness ratio, but all blast variables changed based on the stiffness ratio of a blast. The table at the top of page 58 was developed to help illustrate the differences in blast performance based on stiffness ratio, demonstrating that the goal should be to have a stiffness ratio of between 3 and 4 for a mining environment. In construction, we typically aim for a stiffness ratio of 3.5 or above for even better control due to the sensitive blast nature. The best cost environment for a mine is typically between a stiffness ratio of 3 and 4. This results in the best performance and the lowest drill-and-blast cost from a pure design standpoint in most cases.

The stiffness ratio is defined as the blast’s bench height divided by the blast’s burden. If the bench height is constant, then the smaller the blast’s burden, the higher the stiffness ratio will be. This means the smaller the borehole diameter, the higher the stiffness ratio and the better performance.

Still, there is a limit to this. A stiffness ratio above 4 does not provide any major improvements to blasts in terms of economics or performance. The longer the drill steel becomes based on the diameter, the more drill deviation occurs. In this manner, there is a limit to the performance.

On the opposite side of this, the larger the drill steel is, the larger the burden. This reduces the stiffness ratio and leads to poor performance, including an increase in oversize. Thus, bigger is not always better when it comes to drilling and blasting.

South Africans confirm stiffness ratio

(Photo: Anthony J. Konya)

In this example, a bench with a low stiffness ratio generated 600 percent more oversize than a bench with a high stiffness ratio. Click to expand.

While the term “stiffness ratio” was new when Konya coined it in the late 1960s, the fundamental concept of longer benches producing better results was established much earlier.

In the 1870s, texts on blasting discussed that long benches performed better than short benches – with no real metric defining what was meant. The early 1900s brought blasting texts that described how if the bench height was less than two times the burden, control of the blast would be lost. This, again, was an early primer to the stiffness ratio concept that is used today.

A researcher named Kuznetsov from the Soviet Union found that powder factor was not a major factor in the fragmentation of blasting, but that the geometry of the charge was significantly more important. This “geometry” was actually related to the stiffness ratio of the blast.
Kuznetsov’s work was the introduction into predicting blast fragmentation and, eventually, was incorporated into the Kuz-Ram model when the Roslin-Ramler formula was combined with Kuznetsov’s earlier work and developed a full-scale blast fragmentation prediction model.

The Kuz-Ram model was developed in a similar timeframe as Konya’s stiffness ratio concepts. While developed at similar times, they were developed on two separate continents and for two entirely different reasons.

The Kuz-Ram model was to predict fragmentation, whereas stiffness ratio was to design better blasts. They, however, came to nearly the same conclusions. A low stiffness ratio leads to more oversize, and a high stiffness ratio leads to less oversize.

The first comparison will be between a stiffness ratio of 4 and 1. You can see the percent passing in the figure below. This means the percent of the material is smaller than this size. These two benches have identical explosive products, drill diameters, burdens and all other design variables, which are not affected by the stiffness ratio. The difference between the two is the bench height, or what today is called the stiffness ratio.

The chart shows that with the same design, the bench – which has a stiffness ratio of 4 – has a maximum size of about 48 in. Based on this design, we would expect no rock above 4 ft. in diameter. If oversize was considered rock larger than 3 ft. in diameter, then the bench with a stiffness ratio of 4 would have less than 5 percent of material considered oversize.

Still, the low bench –which has a stiffness ratio of 1 – has more than 10 percent of material larger than 100 in. in diameter (8.5 ft.). This results in a large amount of oversize in the blast. In fact, with the same 3-ft.-diameter criteria for oversize, 30 percent of the material is now considered oversize. In this example, a bench with a low stiffness ratio generated 600 percent more oversize than a bench with a high stiffness ratio.

(Photo: Anthony J. Konya)

This comparison between a stiffness ratio of 3 and 4 illustrates that the difference in fragmentation, while measurable, is fairly minimal. Click to expand.

Ideal stiffness ratio for oversize

With the ideal stiffness ratio for a mine looking to combat oversize being between 3 and 4, the difference between a blast with a stiffness ratio of 3 and one with 4 results in small changes to the fragmentation. This, however, can result in larger cost differences when analyzing the full mine-to-mill picture.

In this event, the goal should always be to aim for a minimal stiffness ratio of 3 and typically no greater than 4 for a mine.
In the chart above, we can see the comparison between the stiffness ratio of 3 and 4. The chart illustrates that the difference in fragmentation, while measurable, is fairly minimal. Using the same 3-ft. diameter for oversize, the blast with a stiffness ratio of 4 would result in 5 percent oversize, and a blast with a stiffness ratio of 3 would result in about 7 percent oversize. While oversize does increase as the bench height is decreased, it is fairly minimal between these ranges.

It is also important to note that all of these blasts have essentially the same powder factor. In this case, the powder factor does not cause a major change in the oversize, but the actual geometry of the bench does. This is exactly what has been found for the last 150 years in blasting. The blast geometry and pattern are significantly more important than just throwing more pounds in a borehole.

So, while a bigger drill diameter may result in some lower upfront costs, it can also result in more oversize and worse blast performance across the board. At least in drilling and blasting, bigger is not always better.


Anthony Konya is vice president at Precision Blasting Services, consulting around the world in rock blasting and vibration from blasting. He is also the founder and CEO of Academy Blasting, an explosive engineering education company, and the host of AcademyBlasting.TV podcast.


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