The blasting quality and the rock volume blasted directly affect the cost of mines. A small charge-forward blast crater experiment was conducted to study the relationships between the rock volume blasted, the explosive unit consumption, the bulk yield, and the depth ratio. The results showed that the rational resistant line or explosive charge depth should be 0.86 times the optimal resistant line. Based on theoretical analysis of the large spacing of the holes and the small resistance line, the uniform design method was used to conduct the lateral blasting crater tests. The relationship equations among the blasting parameters, the blasting volume, and the bulk yield were obtained by regression analysis. The results illustrated that the rock volume blasted was negatively correlated with the bulk yield. The contribution rates of the resistance lines and the spacing of the holes to the blasting volume regression were 32.4% and 13.9%, respectively, and to the bulk yield regression were 65.0% and 0.256%. The impact of the resistance line on the blasting volume and the bulk yield was more significant than that of the spacing of the holes. The blasting effect of the rectangular blast hole arrangement was better than that of the square pattern. The blasting technology of large hole spacing and a small resistance line could achieve a better blasting effect while ensuring a higher rock volume blasted. The economical and reasonable blasting parameters were determined as the hole spacing of a=8.5 m and the resistance line width of W=5.5 m, with the rock volume blasted of 413.1 m3 and the bulk rate of 0.218%. This method provides an effective method for optimization of the blasting parameters and has important guiding significance for efficient and economical mining.
In the mining process, open pits are often faced with the problem of balancing the blasting quality and the volume of rock blasted. If the blasting quality is poor, the large block rate is high, and the block size is not uniform, it will bring difficulty to the loading and crushing work, resulting in an increase in production costs. If the blasting quality is good but the blasting volume is often low, then the overall cost is still relatively high.
Therefore, obtaining a better blasting quality, reducing the bulk rate, reducing the unit consumption of explosives, and controlling the overall cost are the actual technical problems that must be resolved under the condition of ensuring a high blasting volume. The scientific determination of reasonable blasting parameters is the key to obtaining a good blasting effect. In the blasting design, the blasting parameters are generally selected with reference to the similar conditions for the mine; this approach has certain limitations and often has a certain deviation from the actual site. Usually, the blast parameters are not the same, even if the same type of explosive is used, because of the different rock characteristics. It is well-known that Livingstone’s blasting crater theory plays an important role in finalizing the blast parameters [
Many experts and scholars have conducted many research studies to reduce the blasting cost in the mines; such studies can be categorized into three types. The first type is blasting crater theoretical analysis. Mr. W. L. Fourney conducted a study of the crushing mechanism of the blasting crater. The mechanism of fragmentation was one in which the material between the borehole and the free surface is greatly weakened by the stress waves over the first 50
It could achieve a better blasting effect with the method of parameter optimization [
The tests aim to explore the blasting crater parameters and seek the reasonable blasting resistant line to improve the blasting quality, reduce the explosive consumption, and increase the explosive usage efficiency. The experiments were conducted on a +24 m bench in an open pit, where the rock was rich in cracks with the hardness of f=12 to 16 and unit weight of 3.4 t/m3. The diameter of the blasting holes was 250 mm, with the explosive charge of 12 kg per blast hole. The depth of the explosive was 1.5 to 3.9 m. To eliminate the interaction between the adjacent holes, the distance between two holes that were in the same row was more than 15 m.
The parameters of crater sizes to be measured are the crater radius, the crater volume, and the crater depth; it is commonly accepted that the first two can well reflect the characteristics of a blasting crater. The crater parameters are shown in Figure
Distribution of the locations of the explosives.
Measurement of the crater radius.
The explosive depths were chosen from 1.5 m to 3.9 m. Table
Field experiment results.
No. | Explosive depth L/m | Depth ratio△ (L/Le) | Crater depth H/m | Crater radius | Crater angle | Crater volume | Explosive consumption (kg/m3) | Remarks |
---|---|---|---|---|---|---|---|---|
1 | 1.5 | 0.38 | 1.7 | 2.0 | 99.3° | 7.12 | 1.69 | |
2 | 1.8 | 0.46 | 2.0 | 2.2 | 95.4° | 10.14 | 1.19 | |
3 | 2.1 | 0.54 | 2.4 | 2.4 | 90.1° | 14.46 | 0.83 | Optimal explosive depth Lj |
4 | 2.5 | 0.64 | 2.2 | 2.0 | 84.5° | 9.22 | 1.32 | |
5 | 2.9 | 0.75 | 1.9 | 1.6 | 80.2° | 5.09 | 2.38 | |
6 | 3.3 | 0.84 | 1.3 | 1.1 | 75.1° | 1.36 | 9.09 | |
7 | 3.9 | 1.00 | Max. explosive depth Le |
The relationship between the characteristics of the crater V/Q (the crater volume blasted by unit explosive charge) and the depth ratio △ is shown in Figure
Curve of V/Q versus the depth ratio.
Curve of the consumption of explosives versus the depth ratio.
The maximum explosive charge depth was 3.9 m. With increasing depth ratio, the crater volume blasted by unit explosive V/Q demonstrated a trend of first increasing and then decreasing. When the explosive depth was at the optimal value of 2.1 m, the value of V/Q reached the maximum of 1.21 m3/kg, with the crater volume blasted of 14.46 m3. With increasing depth ratio △, the unit explosive consumption showed a trend of first decreasing and then increasing. V/Q reached the minimum of 0.83 kg/m3 when the optimal explosive charge depth was 2.1 m. The bulk yield reached the maximum of 0.82% at the explosive depth of 2.1 m (or at the optimal resistant line), as shown in Figure
Curve of the bulk yield versus the depth of the explosives.
Obviously, the volume of rock blasted and the blast quality are interassociated and mutually conflicting; thus, it is necessary to balance the relationship between them, as mentioned above. From the perspective of the explosive usage efficiency, the explosive energy implied on the rock crushing is a maximum when the crater volume blasted is the maximum with the minimum unit explosive consumption. From the perspective of the mining operation, the blasting quality directly affects the efficiency of the loading, transportation, and crushing, which requires that the bulk yield should be controlled and the rational resistant line must be found.
In summary, the depth ratio must be modestly reduced; i.e., the resistant line should be decreased to guarantee the reasonable resistant line and thus modify the blasting quality in the mining operation. In other words, the optimal blasting quality should be obtained with the premise of achieving a relatively high volume of rock blasted. Based on the analysis above, the reasonable resistant line or the explosive charge depth should be 0.86 times the optimal resistant line, from which the advantage of the reduced resistant line can be enjoyed.
Research studies have shown that when a few waves propagate in a medium at the same time, whether they meet each other or not, they maintain the original characteristics, including frequency, wavelength, amplitude, and vibration direction. Moreover, they are not affected by other waves. The vibration of any particle in the meeting area is the synthesis of the vibration caused by each wave at this point. This rule is called the wave superposition principle or the independent propagation principle of the wave, as shown in Figure
Wave superposition principle.
When two waves of the same frequency are superimposed, the vibrations in some areas are strengthened, the vibrations in some areas are weakened, and the vibration-enhanced area and the vibration-reduced area are separated from each other. This phenomenon is called wave interference [
Wave interference.
Assuming the two wave sources are both simple harmonic vibration, they can be described as follows:
If the one wave travels along r1 and the other travels along r2, meeting at a point P in the same medium (see Figure
Two waves meet at point P.
According to the principle of wave superposition, the combined vibration at point P is the synthesis of these two partial vibrations. The combined vibration equation is expressed as
The combined vibration is still simple harmonic vibration given by
Thus, we have
When
When
The blasting technology of large hole spacing
Mechanism of the large hole spacing with a small resistant line (a2>a1; W2<W1).
It has been proved that this technology is effective in improving the blasting effect, reducing the unit consumption of explosives, increasing the amount of detonation, and reducing the blasting cost, as has been well recognized by experts both at home and abroad.
The blasting mechanism is as follows.
Uniform design is also called Uniform Design Experimentation. Uniform design was jointly proposed by Professors Fang Kaitai and Wang Yuan of the Applied Mathematics Institute of the Chinese Academy of Sciences in 1978. Uniform design is an application of the “pseudo-Monte Carlo method” in number theory.
Uniform design is implemented through a set of well-designed tables and only considers the test points evenly distributed within the test range. The experimental points are well balanced and dispersed within the scope of the test, but they still reflect the main characteristics of the system. Uniform design can greatly reduce the number of experiments and can achieve the test results by performing at least one test of orthogonal design.
Because the test results do not have the orderly comparability of the orthogonal test results, the regression analysis method is used for the processing of the test results. Using the model derived from regression analysis, the importance of influencing factors can be analyzed. Moreover, the new conditional tests can be estimated, predicted, and optimized. At present, this method has gained international recognition and has been widely used in fields such as aerospace, chemical engineering, pharmaceuticals, materials, automobiles, and the environment at home and abroad [
To ensure the high volume of rock blasted with favorable blasting quality, the density of blasting holes must be considered to obtain the optimal combination of hole spacing and the resistant line. The experiments were conducted in the Heshangqiao open pit of Nanshan Mining Company, where the rock hardness is f=8 to 12 and the rock has good integrity. The diameter of the holes was 200 mm, with the depth of 12.5 m and explosive charge of 180 kg per hole. The rock emulsion explosives used were produced by Maanshan Jiangnan Chemical Co., Ltd. The explosive diameter was 170 mm, with a density of 1.10 g/cm3 ~ 1.35 g/cm3. The detonation speed was ≥3200 m/s.
To reduce the number of experiments performed and reduce the effect on mine production, the uniform design method was implemented. Two holes were initiated simultaneously in each experiment. The program of two factors and five levels was chosen. The two factors were the hole spacing and the resistant line width. The hole spacing was from 6 m to 10 m, and the resistant line width was from 5 m to 7 m. A total of five tests were conducted. Based on the application table of uniform design, the U5(52) test schedule was produced, as shown in Table
Evenly designed U5(52) experiment schedule.
No. | Holes spacing/m | Resistant line/m |
---|---|---|
1 | 6 | 5.5 |
2 | 7 | 6.5 |
3 | 8 | 5 |
4 | 9 | 6 |
5 | 10 | 7 |
Blast hole layout.
A picture of the field experiment is shown in Figure
Picture of the field experiment.
Blasting effect.
The experimental results are presented in Table
Experiment results.
No. | Holes spacing | Resistant line | Rock volume blasted Q/m3 | Crater angle | Explosive consumption (kg/m3) | Bulk Yield/% |
---|---|---|---|---|---|---|
1 | 6 | 5.5 | 338.3 | 98° | 0.532 | 0.21 |
2 | 7 | 6.5 | 463.6 | 106° | 0.390 | 0.33 |
3 | 8 | 5 | 350.4 | 104° | 0.519 | 0.18 |
4 | 9 | 6 | 467.1 | 113° | 0.392 | 0.25 |
5 | 10 | 7 | 670.0 | 115° | 0.275 | 0.42 |
The choice of regression equation has an important influence on the research results. Through comparative analysis of each built-in equation, the equation with the highest coefficient of determination, R2, is chosen as the objective equation of this paper under the condition that the regression equation is significant.
Through the multiple factors regression analysis of the experiment results, regression coefficients b(i) were
Thus, the regression equation for the rock volume blasted was obtained.
where
The regression analysis coefficients are shown in Table
Regression analysis coefficient.
Name | 1 | 2 |
---|---|---|
Regression coefficient b(i) | b | b |
Standard regression coefficient B(i) | B | B |
Partial regression square sum U(i) | U | U |
Partial correlation coefficient | ||
Multiple correlation coefficient | R=0.9940 | R2=0.9881 |
Regression square sum: | U=7.03e+4 |
Regression analysis coefficient of equation (
The regression formula produced the following significant results: sample N=5, significance level
Sorted by the partial regression quadratic sum, the contributions of the resistant line and the hole spacing were 32.4% (U
The regression coefficient b(i) was
The bulk yield formula was the following:
where
The regression analysis coefficients are shown in Table
Regression analysis coefficient.
Name | 1 | 2 |
---|---|---|
Regression coefficient b(i) | b | b |
Standard regression coefficient B(i) | B | B |
Partial regression square sum U(i) | U | U |
Partial correlation coefficient | ||
Multiple correlation coefficient | R=0.9858 | R2=0.9717 |
Regression square sum: | U=3.68e−2 |
Regression analysis coefficient of equation (
The regression formula produced the following significant results: sample content N=5; significance level
The contributions of the resistant line and the hole spacing (sorted by the partial regression quadratic sum) were 65.0% and 0.256%, respectively. The resistant line’s contribution was greater than that of the hole spacing, demonstrating that the resistant line had a greater impact on the bulk yield. The reduction of the resistant line and increase of the hole spacing are beneficial to controlling the bulk yield.
Considering that the resistant line has a greater impact on the volume of rock blasted and the bulk yield than the hole spacing, reasonably reducing the resistant line and increasing the hole spacing at the same time can obtain favorable blasting quality with a high volume of rock blasted. Thus, the technology of large hole spacing and a small resistant line is reasonable and practical.
The objective function of total mining cost is
where C1 is drilling cost, C2 is blast cost, C3 is shovel and loading, C4 is transport cost, and C5 is crushing cost.
The blasting effect not only reflects the accuracy and rationality of the blasting design parameters and the blasting methods but also directly affects the subsequent processes, such as shoveling and loading, transportation and crushing, and the total mining cost.
In general, the costs of drilling and blasting increase with the decrease of blasting quality, and the operating costs of subsequent processes decrease with the improvement of blasting quality. In theory, there is an “optimum blasting effect” that makes the total mining cost the lowest (see Figure
Blasting quality and mining cost.
By comparing Figures
Curves of the resistance line, blasting volume, and bulk yield (hole spacing
Curves of the resistance line, blasting volume, and bulk yield (hole spacing
Moreover, if the resistance line is too large, it is difficult to blast the rock, making it not conducive to the formation of a good free surface. Therefore, under the premise of ensuring a higher blasting volume, while the blasting effect is improved, the blasting method of large hole spacing and a small resistance line is suitable.
According to many years of production practice of the Heshangqiao iron mine, comprehensively taking the efficiency of loading/crushing and the total mining cost into consideration, the reasonable and economical blasting parameters are as follows: the hole spacing
Figures
Figure
Curve of the same blasting area of 46.75 m2.
The blasting quality and volume of six perfectly square patterns were compared, as shown in Table
The blasting quality of six perfectly square patterns.
Number | Holes spacing/m | Resistance line/m | Blasting area/m2 | Rock volume blasted/m3 | Bulk yield/% |
---|---|---|---|---|---|
1 | 4 | 4 | 16 | 146.0 | 0.067 |
2 | 5 | 5 | 25 | 252.7 | 0.156 |
3 | 6 | 6 | 36 | 383.0 | 0.266 |
4 | 6.837 | 6.837 | 46.75 | 510.3 | 0.373 |
5 | 7 | 7 | 49 | 537.1 | 0.396 |
6 | 8 | 8 | 64 | 714.8 | 0.546 |
The blasting quality of square patterns.
For the perfect square
It can be seen that blasting quality of a rectangle is better than that of the square pattern. The rectangle of
The data used to support the findings of this study are available from the corresponding author upon request.
The authors declare no conflicts of interest in preparing this article.
This work was supported by the National Key R&D Program of China (no. 2017YFC0602902), the National Natural Science Foundation of China (no. 51674229 and no. 51374189), and the Fundamental Research Funds for the Central Universities (no. WK2480000002). The authors acknowledge their financial support of this work.