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Calculating the Explosive Load Based on Spacing.

This is the third in a three-part article about Precision Presplitting. –Ed.

In the past two articles the authors have thoroughly discussed precision presplitting design and applications. To recap, a precision presplit is a specialty way of presplitting rock to avoid overbreak of the final wall and to create just enough energy to crack the rock. In the past issue, the design of a precision presplit on a 24-in. spacing was discussed. A 24-in. spacing is the common spacing often used for designing a precision presplit in construction blasting with smaller drilling rigs.

The mining industry typically utilizes larger drill rigs which create a larger drill-cuttings cone surrounding the blast hole making it difficult to use 24-in. spacing. In other situations, a spacing less than 24 in. can be used for better control and less overbreak. The goal is then to determine what explosive load (in grains per ft. of detonating cord) will mimic the results of 24-in. spacing.

For calculating the explosive load based on spacing, each rock will be given a unique presplit constant (K) which is related to the Young’s Modulus of the rock. These are shown in Table 1 below for some example rocks, others can be interpolated based on their Young’s Modulus.

F3 1 Table1

From this a model can be made analyzing the stresses around adjacent boreholes with the explosive energy at a set spacing. This results in unique equations for each rock type based on the presplit constant (K). For these five example rock types, a graph has been created for the explosive load at variable spacing, which is shown below in Figure 1.

These graphs are for dry holes and loading with a ½-lb. cast booster or chub of emulsion at the bottom of the borehole with either delayed or instantaneous firing. For wet holes this graph can also be used, with slight adjustments during test blasting. It is not recommended to go beyond a 60-in. spacing, and the larger the spacing the higher the chance for radial cracking on the back wall.

F3 2 Figure1

This graph shows the equations for the competent, average rock sample of each group. From this, along with rock mechanics reports, the values can be adjusted for an “optima”’ explosive load; however, the best way to use this graph would be to find the desired spacing and approximate rock type. Then find the explosive load to use and through test blasting analyze the performance of the final wall.

Once the explosive load and spacing have been designed, one must analyze the environmental affects the precision presplit will have. The two major concerns from this are air overpressure and ground vibration.

In normal blasting operations, air overpressure is not a large concern and regulations are rarely exceeded. However, in the United States a new form of regulating is emerging where structural or physical damage is not the concern but the annoyance of neighbors can be the limiting factor on air overpressure. In addition, precision presplitting generally has higher air overpressure levels than a regular production blast at the same scaled distance.

Air overpressure has a different scaled distance than normal ground vibration, where air overpressure scaled distance is:

F3 eq1

For this equation, the charge per delay is measured in pounds. To accurately estimate this the detonating cord used in precision presplitting must be converted to pounds. This can be done by dividing the grains of detonating cord by 7000 which is shown in the equation below:

F3 eq2

Now that an accurate air overpressure scaled distance can be calculated one can use the chart below (Figure 2) to estimate the maximum air overpressure from a precision presplit. The graph below is shown on logarithmic scale with the vertical (y) axis having a maximum value of 200 and a minimum of 100.

F3 Figure2

The next environmental concern is the ground vibration from a precision presplit. From a normal presplit, the common assumption is that it can be five times greater than a normal production blast. The authors conducted a study to predict the ground vibration from precision presplitting and production blasting to create a comparison. What was found was that the ground vibration from a precision presplit at lower scaled distances was less than a production blast, and at the higher scaled distances was slightly more.

Ground vibration follows the typical square root scaled distance which is shown below:

F3 eq3

Again the conversion to pounds instead of grains must be used. After a scaled distance is found, one can use the chart below to calculate the ground vibration from a precision presplit (Figure 3).

F3 Figure3

An example of how one can apply these methods to design a Precision Presplit. The scenario for the design is:

  • Limestone Surface Quarry with 30-ft. benches.
  • Residential Structures at 1,000 ft.

    – 132 Db Maximum Air Overpressure.

    – 2 in./s maximum ground vibration.

  • 4-in. drill hole.
  • Closest drill spacing is 30 in.
  • No subdrill on presplits.

To begin, the explosive load for limestone at a 30-in. spacing must be calculated. Using the graph in Figure 1 this is an explosive load of about 850 grains per ft. of detonating cord. With a 4-in. borehole approximately 40 in. (3.33 ft.) of stemming will be used.

Then the total powder column must be calculated, this is the total drillhole length minus the stemming height (30 ft. – 3.33 ft.). This gives a total powder column of 26.67 ft. which will be loaded with detonating cord of 850 grains per ft. This is a total of 22,700 grains of detonating cord per hole.

Once converting the detonating cord from grains to lb. (3.24 lb.) and adding a ½ lb. booster in the bottom of the hole, the total explosive load per hole is 3.74 lb. per delay. From this the air overpressure and ground vibration scaled distances can be calculated. These are:

Using the environmental prediction graphs (Figure 2 and 3) one can predict the maximum air overpressure and ground vibration.

  • Maximum Air Overpressure = 128 Db.
  • Maximum Ground Vibration = Less than 0.2 in. per second.

This also illustrates how in a precision presplit the concern, in general, is not the ground vibration but the air overpressure.

In this final article on precision presplitting, graphs have been given to estimate the explosive load at any multiple spacing distances in different rock types. The presplit constant (K) has also been given for various rock types. If a presplit is desired in different rock types the coefficient and explosive load curve can be estimated based on the young’s modulus of the rock.

In addition to the explosive load chart, predictions for air overpressure and ground vibration from a precision presplit have also been discussed. In the example shown, it is mentioned that the major environmental concern from precision presplitting is not the ground vibration but the air overpressure.

Dr. Calvin Konya is the president of Precision Blasting Services, and Anthony Konya is a project engineer for the company.