Blasting mechanics revisited: Blasting design standards

By and |  February 21, 2019
Richard Ash presented key ratios 56 years ago that could be applied throughout surface blasting conditions to give comparisons between multiple types of operations. Photo:

Richard Ash presented key ratios 56 years ago that could be applied throughout surface blasting conditions to give comparisons between multiple types of operations. Photo:

It is not just enough for one to understand what happens during a blast. The most important thing to the average person is to know how blast variables can be controlled to suit the requirements of the operation.

In blasting, a number of variables are easily under the control of the blaster, including the burden, spacing, stemming, subdrill, and timing. In order to simplify these dimensions, ratios are created that could easily be understood and scaled to any operation.

In 1963, five key ratios were presented that could be applied throughout surface blasting conditions to give comparisons between multiple types of operations. Richard Ash denoted these as k-factors, which were the starting point for simplistic blast design.

These could easily be used to get approximate starting points for various situations. The ratios are presented below, with updates for modern-day understanding:

1. Burden ratio (KB). This is the ratio of burden (in feet) to the diameter of the explosive (in inches) due to the fact that typically the burden will be scaled based on the diameter of the explosive.

2. Hole-depth ratio (KH). This is what we understand today to be called the “stiffness ratio” of a blast, and it is the ratio of the bench height of a blast to its burden.

3. Subdrill ratio (KJ). This is the ratio of the subdrill compared to the burden.

4. Stemming ratio (KT). This is the ratio of the stemming length compared to the burden of the blast.

5. Spacing ratio (KS). This is the ratio of the spacing to the burden.

These ratios will be analyzed within this article in greater detail, comparing what Ash wrote in 1963 to what we understand today.

Burden ratio

The most critical and important dimension in blasting is that of the burden.

The choice in burden will ultimately affect the entire performance of the blast. This is due to the fact that the burden dimension is the first step to designing the proper confinement for a blast.

Should the burden be too large, the explosive will never break the rock. If it’s too small, then the explosive will throw the rock across the pit.

The burden ratio of a blast can be used to help determine what an appropriate burden is compared to the hole (or explosive) diameter. However, the actual value of the burden will depend on a combination of the rock characteristics, structural geology, type of explosive, and efficiency of the utilization of the explosive. While the burden ratio can be monitored, it is more critical to observe how variations of this ratio change the outcomes of the blast.

The burden ratio from 1963 to today typically ranges between 20 and 40 depending on the exact situation. In the most basic form, a blast that uses a burden ratio of 20 may experience significant throw and good fragmentation. A blast that uses a burden ratio of 40 or more may experience some breakage (typically into larger boulders) and no movement. This would be considered the maximum effective burden of a blast.

Typically, a mine will not want to blast at the maximum effective burden because the rock will break into large boulders and be difficult to dig. The blasters will then reduce the burden into a more normal range, where proper movement and breakage occur.

In 1963, Ash acknowledged that many variables go into the burden and that the development of the burden ratio was to give the blaster an easy tool to design the burden in the field. At the time, burden formulas were complex and required knowledge of the rock’s Young’s modulus and tensile strength, as well as knowledge of the inter-borehole pressures created by the explosive.

Not only did the blaster not have this information, but, in many cases, the technical representatives and top explosive scientists of the time did not fully understand these. Ash wanted a more appropriate and easy-to-use method to estimate burden that would actually be used. Later, Calvin Konya refined this method and developed easy-to-use equations that could be solved on the back of an envelope but keyed in the burden further, while still scaling with the borehole diameter for bulk explosives and by explosive diameter for cartridge explosives.

Generally, the use of a burden ratio of 30 typically provides the blaster with satisfactory results for the average field condition. With the use of lower density explosives such as ANFO, a burden ratio of between 20 and 25 was recommended. Today, the ratio of 24 is typically recommended for ANFO in average rock.

In 1963 water gels and dynamites were frequently used in blasting, and the recommended burden ratio for these products was between 30 and 40 – typically near 40 for the average rock. With the invention of emulsions, the recommended ratio is now around 30 to 36 depending on rock conditions.

Using a smaller ratio will result in better breakage and greater throw. The final value, though, should be a result of adjustments made based on the goals of the mine.

For example, assume three different companies are blasting in the same rock type using all the same conditions. Company 1 may blast for construction purposes and need to use a smaller burden ratio to gain better control and break the rock finer to dig with small excavators.

Company 2 may be a quarry that will use a slightly larger burden ratio than Company 1, because they can have a larger fragmentation size that will be moved by a loader and haul trucks that can carry 40 tons in a load. Company 3 may be a large metal or coal mine that has large shovels and haul trucks that can easily haul 300 tons at a time. This company may have an even larger burden ratio because the equipment facilitates larger rocks than Companies 1 and 2. The burden ratio must ultimately be adjusted and determined for each specific site, not only based on the site and explosive conditions, but also on the goals of the site.

Hole-depth ratio

The hole-depth ratio is now considered the stiffness ratio of a blast. Since blasting was first studied in the 17th century, it has been understood that a low bench will blast poorly compared to a high bench.

In the late 1800s, it was discovered that when a bench was the same height as the burden distance, or shorter, the blast was unable to be contained. This later developed into the hole-depth ratio, in which Ash recommended that the length of the bench should never be less than the burden dimension.

The term “stiffness ratio” was coined by Calvin Konya in the mid-1960s. Konya and Ash then recommended that the stiffness ratio should not be less than 2. In practice, the stiffness ratio of a blast is typically between 1.5 and 4, with the highest frequency of around 2.6.

At a stiffness ratio of 1 a blast will crater, meaning the blast will display violent blowout with rock ejected vertically. The blast will break under the borehole effect at a stiffness ratio of 4. This will be observed through the bending (flexural failure) of the blast and horizontal displacement.

The borehole effect provided the proper placement and movement of the muckpile and allows for better fragmentation of the rock mass. As the stiffness ratio is reduced (closer to 1), the cratering action will become more prevalent. As it is increased, the borehole effect will become more prevalent. Blasts can be fired with a stiffness ratio greater than 4 without adverse effects as long as drill hole accuracy is maintained.

Subdrill ratio

The primary reason for subdrilling below floor level is to ensure the full bench will be removed without a toe or hump left on the floor. The 1963 recommendation was that the subdrill ratio should never be less than 0.2 and typically was around 0.3. The only exception to the rule was this: If there was a good bedding plane or weak seam at the grade of the floor, then the subdrill was not needed for a vertical borehole.

Today, it is understood that a subdrill is required at a majority of operations and the safe ratio to use is 0.3. Still, this ratio will be altered not only based on the geology but also based on the stiffness ratio. A low bench, with a stiffness ratio around 1, may never pull to grade between borehole due to the breakage mechanism. A high bench with proper bottom priming may only need a ratio of around a 0.2.

In addition, products exist today claiming that if they are used in the subdrill of a blast, the explosive does not need to be used in the subdrill and the bench will still break to grade. In situations where a product works well, the bench probably did not need explosive in the subdrill anyway and would have broken. This is due to an interaction of geology and the burden design – not the stick in the bottom of the borehole.

Stemming ratio

The stemming, or collar, of a blast refers to the inert material that is placed on top of the explosive charge in order to confine the explosive energy. Studies on stemming have shown that when the stemming is completely removed from the borehole, either through design or inadequate stemming that blows out prematurely, the maximum effective burden can be reduced by more than 30 percent.

This simple concept can show just how important the stemming and retention of the gas pressure is in a blast. Ash recognized this in the 1960s.

“The use of stemming material then assists in confining the gases by a delayed action that should be long enough in time to permit their performing the necessary work before rock movement and stemming ejection can occur,” Ash stated.

Even back then, with confusion on the role of shockwaves in blasting, Ash observed how critical it was for stemming to properly confine explosive gasses. The actual effect of stemming is not in changing the way that the explosive functions, but in increasing the efficiency of using explosives in a borehole by partially sealing it. The stemming should hold not only until the rock is fractured, but until face movement begins and the borehole is naturally depressurized through the fractures in the rock.

Today, it is understood that crushed gravel is the preferred material for stemming, as it provides both internal stresses where bridging of the material occurs. It also creates a plug that has shear strength, providing resistance from blowout.

Drill cuttings, water, concrete, plaster and other methods are not preferred because they lack these properties and are considered inadequate stemming.

Stemming plugs on the market today can improve the performance of drill cuttings, but they do not compare to the use of crushed gravel alone as a stemming material.

The rules of thumb on stemming length remain the same as in 1963. The stemming ratio should be about 0.7 when using crushed stone; when using other materials, the stemming ratio should be 1.0 to 1.2. This may still result in blowout of the boreholes.

Spacing ratio

Commercial blasting typically requires the use of multiple blastholes, making it necessary for blasters to know whether or not there are any mutual effects between charges.

The effect between boreholes is determined by the spacing ratio of a blast. Blasters often do not fully consider this spacing ratio. Instead, powder factor or basic design patterns are used.

For example, a blaster may want to use a powder factor of 1.1 pounds per cu. yd. After designing the burden and borehole, the blaster will then set the spacing to give this powder factor. This is a poor method of design, as it is well understood now that powder factor is not an appropriate design tool. It is more of an economic tool.

Another common approach is to use a set pattern such as an equilateral triangle pattern. These patterns typically come into play because they work well in a certain situation by giving the appropriate spacing ratio for the situation.

On a pattern such as the equilateral triangle pattern, the spacing ratio is roughly a 1.15. This is about what would be used for benches around a stiffness ratio of 2.5 and firing each hole delayed. Still, when going to a much higher bench, this pattern performs poorly. Good blasters need to understand this spacing ratio to provide insight in designing a blast to achieve a proper borehole interaction.

In 1963, Ash wrote about the interaction of boreholes that was based on the timing of the blast. Generally, the spacing ratio would vary between 1.0 and 2.0 with the basic rules of thumb being:

1. For extremely long delays, KS should equal 1.0;

2. For hole firing instantaneously along a row, the KS should be equal to 2;

3. For holes firing on a delay, the KS should be between 1.0 and 2.0 – and typically between 1.2 and 1.8.

This is because the blasting is four-dimensional, as timing is a crucial part of the design. Changes in timing lead to different effects and stress fields in the rock.

The spacing and timing then determine the fragmentation. Should the spacing be too close for the timing, fines will occur between boreholes with boulders in the burden of the blast. Should the spacing be too far for the timing, large boulders will be found between boreholes and sawtooth effects can form on the back wall.

Today, it is understood that not only does the timing influence the borehole interaction, but the stiffness ratio of a blast will have a major influence on the spacing. A sliding scale exists where the higher the stiffness ratio (up to a stiffness ratio of 4), the larger the spacing can be.

At a stiffness ratio of 4, the spacing becomes constant and the changes are then only based on the hole-to-hole timing of the blast. This allows the blaster to key in the spacing for a specific blast based on the different design variables. The interaction between timing, spacing and bench height are all reasons that simply using a set powder factor or pattern are not recommended.

It is now understand that spacing is a major factor for both the fragmentation and throw of a blast. As Ash stated in his 1963 paper, “It can be generally assumed that uniformity of sizing is a direct result of the KS ratio. If on firing a single hole the rock is satisfactorily broken and cleanly removed without excessive displacement, it may be assumed the burden is satisfactory. Too often, blasters reduce the burden rather than extend the spacing in their desire to eliminate boulders or to make rock sizing more uniform.”


Most blasting difficulties occur because of a lack in understanding of how rock is broken and the use of improper charge-placement and initiation-timing practices. We’ve explored the basics of blast design for a typical rock, with the exception of blast timing, from 1963 through today. The old standards that Ash recommended in 1963 were:

KB = 20 to 40
KH = 1.5 to 4
KJ = 0.3 (minimum)
KT = 0.5 to 1.0
KS = 1.0 to 2.0

These ratios continue to give blasters basic starting points for blast design, but these are rather large ranges for design. Methods exist today to key in on much more exact numbers and ranges, depending on the goals for fragmentation and throw, relying on the advice of those like Ash who developed these original rules of thumb.

As Ash once stated, “The standards will be found to be quite convenient and useful, after very little practice, not only for the initial design of blasts but also in providing guidelines upon which to correct normal blasting difficulties which invariably occur from time to time. However, one must realize that the standards in themselves are not cure-alls, since blasting as such depends heavily on cost and safety considerations, as well as on the explosive grades used, the material’s characteristics and blasting techniques employed.”

About this four-part series

In 1963, Pit & Quarry published a series of articles on the mechanics of blasting authored by Richard Ash, a longtime professor of mining engineering at the School of Mines & Metallurgy at the University of Missouri-Rolla. The content within each article was ahead of its time, putting forth cutting-edge concepts about the mechanics of rock breakage, standards for blasting design, the characteristics of explosives, and material properties, powder factor and the cost of blasting.

The Academy of Blasting & Explosive Technology, including Anthony Konya and Dr. Calvin J. Konya, pay tribute to the time-honored principles Ash put forth more than 50 years ago with a special 2019 series for Pit & Quarry readers.

In their “Blasting Mechanics Revisited” series, the Konyas look back on Ash’s work and explore how modern-day technology and methods currently fit into each of the areas Ash covered a half-century ago.

Look for these additional articles from the Konyas within P&Q in the months to come:

Part 1. The Mechanics of Rock Breakage (January)
Part 2. Blast Design Standards (February)
Part 3. Characteristics of Explosives (March)
Part 4. Material Properties, Powder Factor, Blasting Cost (April)

Anthony Konya is the senior explosive engineer for Precision Blasting Services who consults around the world in rock blasting and vibration from blasting is and an instructor for the Academy of Blasting and Explosive Technology. Calvin J. Konya is the president of Precision Blasting Services and director for the Academy of Blasting & Explosive Technology, consulting and training worldwide in rock blasting, vibration and emulsion manufacturing.

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