Delay Times

Delay Times

Chapter 16 Delay Times Chapter Outline 16.1 16.2 16.3 16.4 Reasons for a Delay Time 315 16.1.1 Ground Vibrations 315 16.1.2 Rock Damage Nearb...

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Chapter 16

Delay Times Chapter Outline 16.1

16.2

16.3

16.4

Reasons for a Delay Time 315 16.1.1 Ground Vibrations 315 16.1.2 Rock Damage Nearby 317 16.1.3 Seismic Events 317 16.1.4 Rock Fragmentation 317 Factors to be Considered in Determining Delay Time 317 16.2.1 Stress Distribution 317 16.2.2 Crack Propagation 318 16.2.3 Detonation Waves 318 16.2.4 Confinement and Boundary Conditions 319 16.2.5 Rock Fracture Nearby 319 16.2.6 Vibrations in Far Field 319 16.2.7 Movement of Fragments 319 Delay Time in a Single Blasthole 319 16.3.1 One Detonator Position 319 16.3.2 Multidetonator Positions 321 Delay Time Between Two Adjacent Blastholes 321 16.4.1 Background 321 16.4.2 Fragmentation Radius Rfg Smaller Than Spacing S 322

16.4.3 Fragmentation Radius Rfg Equal to or Larger Than Spacing S 326 16.5 Delay Time Between Adjacent Rows 327 16.5.1 Stress Wave Superposition 327 16.5.2 Collision of Fragments 327 16.6 Simultaneous Initiation in Production Blasts 328 16.6.1 Stress Analysis 329 16.6.2 Test Results 329 16.7 Comments on Delay Time 330 16.8 Concluding Remarks 330 16.8.1 Reasons for a Delay Time and Factors Affecting Delay Time 330 16.8.2 Delay Time in a Single Hole 330 16.8.3 Stress Distribution and Delay Time 330 16.8.4 Simultaneous Blasting 331 16.9 Exercises 331 References 331

In order to make rock fracture more efficiently, there are two measures to take. One is to supply more energy to the rock, and the other is to find out a better stress and energy distribution which is favorable to rock fracture while total energy is not increased. In rock blasting the second measure can be realized by choosing a proper delay time. Efficiency is just one of the reasons for employing a delay time in blasting. This chapter will show other reasons why a delay time is often necessary. Then the factors affecting delay time will be discussed. After that, the delay time in a single blasthole, the delay time between two adjacent blastholes, and the delay time between two neighboring rows or rings will be analyzed. Last, a typical delay time—simultaneous initiation of multiholes—will be discussed.

16.1  REASONS FOR A DELAY TIME There are a number of reasons for using a delay time in multihole blasting, such as ground vibrations, rock damage nearby, seismic events, and rock fragmentation. These are to be discussed in the following.

16.1.1  Ground Vibrations Under otherwise identical conditions, a multihole blast with simultaneous initiation will result in much higher ground vibrations than another with a delay time. Take a three-hole blast as an example, as shown in Fig. 16.1. Here we take a simple situation without free surfaces close to the boreholes. Fig. 16.1 indicates that three holes H1, H2, and H3 in a row are initiated at the same time. At location M, the total blast-caused vibrations consist of three vibration waves coming from holes H1, H2, and H3. In the case that vibrations have to be considered, the distance between M and each blasthole is often much longer than the distance between the blastholes. In other words, it can be considered that l1 ≈ l2 ≈ l3. Thus, these three waves Rock Fracture and Blasting: Theory and Applications Copyright © 2016 Elsevier Inc. All rights reserved.

315

316 PART | IV  Basic Parameters of Rock Blasting

FIGURE 16.1  Ground vibrations caused by simultaneous blasting of three holes.

FIGURE 16.2  Ground vibrations caused by delayed blasting of three holes.

are superimposed together almost at the same time. If we have a gauge at location M and it can measure the x direction (or other directions) particle velocity, the total particle velocity in the x direction shown by the dashed curve will be nearly three times higher than one of the three waves in the x direction indicated by the three curves H1, H2, and H3 in Fig. 16.1. Fig. 16.2 shows that three holes are blasted with a delay time which is long enough to separate vibration waves from each blasthole. Similarly, no free surfaces are dealt with. In this case, the total vibrations are the three independent waves, as shown in Fig. 16.2. The highest vibration is equal to the maximum one from each single hole. Notice that if a shorter delay time than the length of the individual wave is applied, the superposition of the three individual waves will happen, and the total vibration may be either higher or lower than any individual wave. As a consequence, a simultaneous blasting of N holes gives rise to nearly N times higher vibrations than a delayed blast if the delay time is long enough to separate any two neighboring vibration waves. Therefore, in a multihole blasting, a delay time is necessary if vibrations must be controlled.

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16.1.2  Rock Damage Nearby As stated previously, a vibration wave is one type of stress wave. A high vibration means high particle velocity if the vibration is measured by a velocity gauge or sensor. Accordingly, a high particle velocity corresponds to a greater stress or strain. In this sense, at any point like M in Figs. 16.1 and 16.2, a simultaneous blasting of multiholes will cause much higher stress or strain than a delayed blasting at M. When M is not far from the blasthole, the simultaneous blasting can produce a very high stress at M and damage the rock there, particularly when the stress is tensile. In contrast, in a delayed blasting of multiholes with a properly long delay time, the superposition of the stresses from each hole can be avoided or reduced. Thus, there is less rock damage caused by the delayed blasting. This is particularly important for underground mining, especially when mining activity goes deeper and deeper. In other words, reduction of blast-induced rock damage to nearby rock structures such as drifts, shafts, and transportation levels will become more and more important in deep mining. More description on blast-induced rock fracture like spalling in underground mines can be found in chapters: Rock Blasting in Underground Mining; Safety in Rock Engineering.

16.1.3  Seismic Events It has been found that many seismic events take place in the blast-influenced zone after blasting, particularly after a massive blast [1]. This means that a massive blast can initiate seismic events. The major reason is that a massive blast releases a huge amount of energy that can easily trigger a seismic event. For example, when N blastholes are initiated at the same time, the stress amplitude in the simultaneous initiation will be N times higher than that in the delayed blasting, as shown in Figs. 16.1 and 16.2. Therefore, the simultaneous blasting of multiholes may to a great extent initiate a potential seismic event, but a delayed blast of the multiholes may not. When mining activity goes deeper and deeper in underground mines, more and more seismic events occur. In order to reduce the seismic events as much as possible, simultaneous blasting from multiholes should be avoided. Furthermore, the scale of blasting, for example, total weight of explosive contained in every individual delay, should also be limited. More discussion on the seismic events related to blasting can be found in chapter: Safety in Rock Engineering.

16.1.4  Rock Fragmentation Previous studies have shown that delay time is related to fragmentation [2,3]. This is because a delay time influences stress superposition in a multihole blasting if the delay time is in a certain range of values. However, it has never been found that a multihole blast with a simultaneous initiation gives rise to a good fragmentation. This will be discussed later in this chapter. Anyway, a delay time between two neighboring holes is necessary in a multihole blasting in which fragmentation is a major concern.

16.2  FACTORS TO BE CONSIDERED IN DETERMINING DELAY TIME To determine a correct delay time for a multihole blasting depends on the purpose of the blasting. When a blasting is to achieve a smooth surface, a simultaneous initiation is a correct delay time, as discussed in chapter: Air Deck and Smooth Blasting. When a blasting is to control ground vibrations, a relatively long delay time between blastholes is one of the good choices. More description on vibration control is to be presented in chapter: Reduction of Ground Vibrations. When a blast is to achieve fine fragmentation, the determination of a correct delay time becomes complicated, unlike in smooth blasting and vibration control. In the following we will discuss the main factors to be considered in determining a delay time for a multihole blasting aiming at good fragmentation.

16.2.1  Stress Distribution In a multihole blasting, if the delay time Td between two neighboring holes is longer than the stress wave length l from the longer hole, ie,

Td > λ

(16.1)

then there is not any stress superposition coming from the two-hole blasting. This case is shown in Fig. 16.3a, in which it is assumed that the two waves are identical. In such a case, a multihole blasting is actually similar to a number of independent single-hole blastings, one followed by another. Thus, there is no superposition of explosive energy from different holes.

318 PART | IV  Basic Parameters of Rock Blasting

FIGURE 16.3  Stress waves in a delayed blast. (a) There is no stress superposition for a long delay time; (b) there is stress superposition for a short delay time.

In contrast, if

Td < λ

(16.2)

a stress superposition will happen from the two holes, as shown in Fig. 16.3b. The final stress wave due to the stress superposition is indicated by a dashed curve, which is copied in the right side, too. It can be seen that the total length of the final wave is greater than that of the single-hole wave. In particular, the final compressive wave due to superposition is much longer than the single compressive wave. A correct delay time will give rise to an effective stress superposition and result in better fragmentation, and vice versa. Note that the stress superposition depends on the waveforms of the stress waves from each single hole. We have noted that delay time is largely dependent on stress wave length l. Furthermore, l depends on charge length, primer position, quantity of primers in a blasthole, velocity of detonation, initiation plan, and so on. Accordingly, these parameters are to be considered in determining a delay time.

16.2.2  Crack Propagation As described earlier, stress distribution is of importance in determining a correct delay time. During rock fragmentation, however, the stress field in the rock mass varies all the time. Especially when a crack is produced, the stress field will be greatly changed due to the propagation of the crack.

16.2.3  Detonation Waves The stress waves in the rock originate from the detonation waves in the blastholes. Consequently, delay time depends on the detonation waves. It is possible to measure the detonation waves. Under the condition that the stress waves are not available but detonation waves are, the parameters of the detonation waves can be used to determine a correct delay time.

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As we mentioned in chapter: Single-Hole Blasting, the detonation wave is usually much longer than the detonation time in a blasthole. Therefore, it is necessary to know the length of the detonation wave to determine a correct delay time.

16.2.4  Confinement and Boundary Conditions In normal conditions, the front surface of a sublevel caving ring is often partly confined by caved waste rock; above the ring are also the waste rocks. In the case where only one ring is blasted each time and a very short delay time which assures an effective stress superposition between two neighboring holes is used, the ore mass in the ring will be well-fragmented but the fragments will be overthrown forward due to strong stress wave superposition or high energy concentration during a very short time. In consequence, the fragments will be mostly thrown away from the ring. At the same time, an empty space between the thrown fragments and the ring to be blasted next time will be created, but this empty space will be immediately filled with the waste rocks over the blasting ring. This is very bad for ore recovery. Therefore, in this case the delay time should not be too short.

16.2.5  Rock Fracture Nearby In rock blasting, particularly underground mining blasting, a possible rock fracture or damage close to a blasting source has to be considered in designing a blasting. In other words, if a delay time is optimal for rock fragmentation, but it may give rise to much rock fracture or damage in the rock structures nearby, we should not choose such a delay time in the operation.

16.2.6  Vibrations in Far Field When ground vibrations in the far field must be controlled, the delay time to be chosen has to ensure that the final vibrations in the disturbed areas are definitely lower than the maximum vibration which is allowed.

16.2.7  Movement of Fragments The movement of fragments from one blasthole influences the blast results of the immediately following blasthole. This is particularly the case in open cut as discussed in chapter: Rock Blasting in Open Cut and Tunneling. For example, after the first-initiated hole is fired, the fragments need enough time to move out of the open room. A correct delay time must be longer than this time. Otherwise, the fragments from the first hole will be jammed by the fragments from the immediately following hole. The preceding description indicates that to determine a correct delay time a number of factors must be considered. These are stress distribution, crack propagation, detonation waves, rock damage nearby, surface confinement, ground vibrations, and movement of fragments. Sometimes a blast operation is mostly limited by one of these factors. For example, when a blast source in a mine is close to an inhabited area, the ground vibrations caused by blasts must be controlled. All in all, these factors should all be considered in determining a delay time. In principle, however, a preliminary determination of delay time can first be based on one of the factors such as stress distribution. After the preliminary determination is done, the determined delay time can be approved or adjusted by using other factors. In the following, we will show a basic process and principle for determining a delay time on the basis of stress distribution. Three cases will be discussed: (1) delay time in a single blasthole with multidetonator positions; (2) delay time between blastholes; and (3) delay time between rows or rings.

16.3  DELAY TIME IN A SINGLE BLASTHOLE In a single hole there are two cases: one detonator position and multidetonator positions. If blast-induced ground vibrations are so high in an inhabited area near a blast source that the high vibrations must be controlled, one detonator position should be used, because multidetonator positions with simultaneous initiation may result in higher vibrations. This has been analyzed theoretically in chapters: Stress Waves; Shock Waves; Primer Placement. Otherwise, if vibrations do not cause any problem and rock fragmentation is the most important task for blasting, it is better to employ multidetonator positions.

16.3.1  One Detonator Position In this case no delay time is involved, so it is just necessary to choose detonator position. We take a production ring as an example in sublevel caving, as shown in Fig. 16.4. In Fig. 16.4, DB, DM, and DC represent three detonator positions near

320 PART | IV  Basic Parameters of Rock Blasting

FIGURE 16.4  A ring in sublevel caving. The shadow represents the fragmentation region of blasthole 5. The detonator positions at the bottom, middle, and collar of the blasthole are shown by DB, DM, and DC, respectively.

the bottom, the middle, and the collar, respectively, of a charged blasthole. The stress wave analysis indicates that the middle detonator position should be beneficial to fragmentation, and this is then proved by production tests showing that the middle detonator position gives rise to better fragmentation, higher ore extraction, and less brow damage, compared with the collar detonator position; see chapter: Primer Placement. This is because the escape of detonation energy from the borehole to the drift is largely reduced in the case of one detonator position. Similarly, the tensile stresses near the brow and in the drift roof become smaller. As a result, reduction of brow damage is achieved. A detailed analysis is in the chapter: Primer Placement As for the bottom detonator position, according to stress wave propagation it can be found that the bottom position is better than the collar position since the escape of detonation energy to the drift and the brow damage can be largely reduced. But some detonation energy may escape into the caved rock on the top of the ring since rock fracture starts there. Therefore, it can be concluded that in view of rock fragmentation and energy utilization, the best choice is the middle detonator position, the worst is the collar position, and the bottom position is in between. For other types of blasting such as bench blasting, the preceding analysis is valid, and the conclusion is suitable, too.

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16.3.2  Multidetonator Positions Multidetonator positions in a single blasthole are often employed in engineering blasting. The delay times in this case can be divided into two kinds: (1) same delay time and (2) different delay times.

16.3.2.1 Same Delay Time If each hole is charged with two or more detonators at different positions and these detonators are initiated simultaneously, the stress waves from these initiation places may be superposed with each other within the rock surrounding the blasthole. Taking a double-detonator position as an example, we can find it has at least three advantages: (1) A shock wave collision happens. This collision gives rise to the final shock wave amplitude becoming greater than the sum of the two single wave amplitudes. In general this should be good for fragmentation. (2) Stress superposition in the rock is much greater than that in a single-detonator position case, since in double-detonator position the detonation propagates at four locations at the same time, but in single-detonator position the detonation travels just at one or two locations. (3) Brow damage and back break can be reduced in sublevel caving. The detailed description on these can be found in the chapter: Primer Placement and in Zhang [4]. The preceding analysis is consistent with production tests [4–6] and field measurements [7]. However, as two or more detonators are placed in a single hole and they are given the same delay time, the detonator position must follow the principles in the chapter: Primer Placement.

16.3.2.2 Different Delay Times A certain delay time is applied to the detonators in a single hole in some mines and quarries so that the detonator close to the collar is taken as a backup. This can be shown by Fig. 16.4 where the detonators DB and DM are ordinary detonators and detonator DC can be taken as a backup. In this case, the ordinary detonators DB and DM are usually initiated first and the detonator DC later. If the two ordinary detonators do not work, the backup detonator will initiate the explosive so as to avoid a misfire. However, if the two ordinary detonators work well, the backup detonator will be a sacrifice. Clearly, such a sacrifice is not necessary. Another drawback of this design is the detonator position close to the collar. As addressed in the chapter: Primer Placement, the collar detonator position should be avoided in all cases of production blasting. To improve the design, it is better to place the backup detonator far from the collar if possible, while its delay time can be kept either the same or not the same as the ordinary detonators in the same hole, depending on whether one wants to have a shock collision.

16.4  DELAY TIME BETWEEN TWO ADJACENT BLASTHOLES 16.4.1 Background Langefors and Kihlström [2] developed an empirical relation between delay time Td in ms and the burden B in meter according to the blast results with burden from 0.5 to 8 m, as follows:

Td = kB

(16.3)

where k is a constant equal to 3–5 ms/m. Then it was reported that an optimum delay time was in a range of k = 3.3–26 ms/m for full-scale tests on the basis of experimental tests [8]. Similar results [9] showed that the optimum delay time was in a quite wide range. It was also argued that neither a too short nor a too long delay time between rows was good for rock fragmentation and muckpile [10]. All of these studies indicate that the so-called optimum delay time is in a wide range of time, but a firm theoretical ground is lacking. As described before, a delay time is dependent on a number of factors. However, Eq. 16.3 shows that delay time is only related to burden by a constant k, meaning that these factors are not distinctly reflected. In the following we will see how to determine a delay time by analyzing the stress wave interaction. The stress and fracture interactions between blastholes happen in a three-dimensional space in reality, so these interactions should be analyzed in a three-dimensional state. Alternatively, the interactions can be analyzed in both vertical (along borehole axis) and horizontal (in cross section of borehole) sections. In order to make the analysis simple, a two-hole blast with a delay time is employed and the analysis is limited to the horizontal section. For the vertical section, a similar analysis can be made. It is assumed that the two holes have the same charge condition and their burden is B. Because in both open pit and underground blasting the blastholes in each row or each ring are usually initiated one by one with a delay time, any single hole exclusive the first-initiated hole in the row or ring has two free surfaces during blasting. As shown in Fig. 16.5, a single row or ring has a free surface EF and hole 1

322 PART | IV  Basic Parameters of Rock Blasting

FIGURE 16.5  Stress wave propagation as t = 2TP +

S after hole 1 at O1 is initiated. cP

at O1 has another free surface FG created by an earlier-blasted neighboring hole in the right side. It is defined that Rfg is the fragmentation radius of a single hole. In the region of Rfg the rock is fractured into discrete fragments. Note that Rfg in practice is much greater than that indicated in Fig. 16.5. In order to show the stress interaction clearly, we drew a smaller fragmentation area. The two-hole blast can be discussed in two different cases: (1) as Rfg of hole 1 is smaller than the spacing S, the distance between both holes, and (2) as Rfg of hole 1 is equal to or larger than S.

16.4.2  Fragmentation Radius Rfg Smaller Than Spacing S In this case, if explosive, detonators, and their initiation do not have any problems, blasthole 2 will be successfully blasted, without any disturbance from blasthole 1. Similarly, if a number of holes are blasted in such a case, all of the holes will be successfully blasted except for sympathetic detonation caused by some geological problem. However, in this case, there are different situations to be described. The following description will show that there is not any kind of superposition of the waves from hole 1 and hole 2 if the delay time



Td ≥ 2TP +

2 S − Rfg cP

(16.4)

where cP is the velocity of the P-wave in the rock and TP is the length of the stress wave caused by blasting in hole 1 (or 2). According to previous studies [7,11] presented in the chapter: Single-Hole Blasting, we take the well-known stress wave form caused by a long hole blasting in rock, as shown by the dark area in Fig. 16.5. This wave form starts from compressive wave TP+ and follows a small tensile tail TP−. Fig. 16.5 shows the distribution of the stress waves as t = 2TP + S/cP after hole 1 is initiated. Here S-waves are neglected. The front and the end of the original P-wave from blasthole 1 are represented by

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the two trimmed circles in Fig. 16.5. The front and the end of the reflected P-wave from free surface EF are indicated by curves EXG and JLG, respectively. The reflected wave from free surface FG is indicated by KMNI. Note that the reflected wave from surface GH should be very small and ignorable. In addition, the boundary GX of the reflected wave is assumed to be a straight line but actually it should be a curve. As t = 2TP + S/cP, we can also see that in the area surrounding borehole 2 two reflected waves from both surface EF and FG meet with each other. At this moment if hole 2 is initiated, the compressive wave from hole 2 will be superimposed by the two tensile waves surrounding hole 2. This kind of superposition is called inefficient superposition. The delay time period corresponding to the inefficient superposition will start as t = TP+ + S/cP after hole 2 is initiated and will be over as t = 2TP + (2S − Rfg)/cP. This can be confirmed by analyzing Figs. 16.5 and 16.7. From Fig. 16.5 we can find as t = 2TP + (2S − Rfg)/cP that the reflected wave indicated by EJLGXE will move away from hole 2, and the reflected wave KMNIK will move to the left side and position N will go to the center O2 of hole 2. The distance between N and O2 is S − Rfg. After this time if hole 2 is initiated, there will not be any kind of wave superposition from the two-hole blasting. Fig. 16.6 shows the wave propagation as t = TP + (S + Rfg)/cP after hole 1 is initiated. After this time, the compressive stress wave due to the initiation of hole 2 will meet with two reflected waves indicated by IJKFLI and XFMNYX, respectively. The latter represents the reflected wave from free surface FG. Fig. 16.7 shows the wave position as t = TP + S/cP after hole 1 is initiated. We can find as TP+ + S /cP ≤ Td ≤ 2TP + (2 S − Rfg )/cP , the original compressive stress wave from hole 1 will not meet the original compressive stress wave induced by hole 2

FIGURE 16.6  Wave propagation as t = TP + ( S + Rfg )/cP after hole 1 is initiated. Inefficient superposition occurs at this time.

324 PART | IV  Basic Parameters of Rock Blasting

FIGURE 16.7  Wave propagation as t = TP + S /cP after hole 1 is initiated. Inefficient superposition occurs at this time.

blasting, but as shown in Figs. 16.5 and 16.6, the original stress wave from hole 2 will be superimposed by the reflected waves of hole 1 from the free surfaces. From Fig. 16.7 we can also find that as Td < TP+ + S /cP, the superposition of the compressive stress waves both from hole 1 and hole 2 will happen. This kind of superposition is called efficient superposition. Such a superposition will happen in the delay time period 0 ≤ Td < TP+ + S /cP. For example, as Td = ( Rfg + S )/cP that is smaller than TP+ + S/cP , the stress wave distribution of hole 1 is shown in Fig. 16.8. After hole 2 is initiated, the compressive wave from hole 1 will meet with the compressive wave from hole 2. Furthermore, as Td = 0 (ie, simultaneous initiation), the superposition of the waves from both holes will reach maximum, as shown in Fig. 16.9. On the basis of the preceding description, the following conclusions can be drawn. 1. If the delay time meets Eq. 16.4, there is not any kind of wave superposition from the two-hole blasting. Under this circumstance a delay blasting is like independent single-hole blasting. In other words, no energy superposition from neighboring holes occurs. If we want to improve energy efficiency and fragmentation, the delay time in this period should be avoided, particularly as electronic detonators are used. We will see two examples: one for the blasting in sublevel caving and the other for bench blasting. In order to make analysis simpler, we assume that in both cases all detonators are placed at the bottom of blastholes; the average length LS of charged blastholes in sublevel caving is equal to 30 m; the charge length of each blasthole in the bench is 10 m; the P-wave speed cP is 4000 m/s; the spacing S is 2 m for sublevel caving and 6 m for open pit mining; Rfg = 1.5 m is for sublevel caving (based on Malmberget mine data) and Rfg = 3.0 m for bench blasting. In addition, according to the chapter: Single-Hole Blasting we assume that

TP ≈ TBP = mBP Tdet = mBP LS /D

(16.5)

where D is the velocity of detonation, TBP is the wave length of borehole pressure, and mBP is a constant determined by experiments. Let mBP = 4 and D = 5000 m/s and substitute all of the values mentioned above in Eq. 16.4 we can get as Td ≥ 48.6 ms in sublevel caving and Td ≥ 17.8 ms in open-pit blasting, there will be no wave superposition in blasting. We note that the wave length TP plays a dominant role in determining Td.

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FIGURE 16.8  Wave propagation as t = ( S + Rfg )/cP after hole 1 is initiated. Efficient superposition occurs at this time.

FIGURE 16.9  Wave propagation as Td = 0 after the two holes are initiated.

2. If the delay time satisfies the following condition

TP+ + S /cP ≤ Td ≤ 2TP + (2 S − Rfg )/cP

(16.6)

inefficient superposition will occur; that is, a compressive wave from one hole will meet with a tensile wave from the other. In this case, the superposition will result in lower stresses in some areas but higher stresses in others. To achieve a successful superposition, it is better not to choose a delay time from this period.

326 PART | IV  Basic Parameters of Rock Blasting

3. If the delay time meets the condition Td < TP+ + S /cP



(16.7)

an efficient superposition will happen, as shown in Fig. 16.8, and the maximum superposition comes as Td = 0 in Fig. 16.9. In order to obtain a better fragmentation or optimum fragmentation, a delay time within this period should be chosen. However, the thing is not so simple in the case of simultaneous initiation or with a very short delay time, since a complicated interaction between an emerging crack and the stress field occurs. It is not necessary for an efficient stress superposition in the simultaneous initiation to give rise to good fragmentation. This will be discussed later.

In summary, in the case of Rfg < S, the delay times meeting Eqs. 16.4 and 16.6 are not suitable for good fragmentation, so they should not be chosen. The delay time satisfying Eq. 16.7 is available to choose for good fragmentation. However, care must be taken when a very short delay time is considered. In particularly, simultaneous blasting should be avoided if blasting is to achieve good fragmentation.

16.4.3  Fragmentation Radius Rfg Equal to or Larger Than Spacing S This is shown in Fig. 16.10. There are two different cases here. 1. Td ≥ Tfs Here Tfs means the time for the fragmentation region expanding from hole 1 to hole 2. In this case, as soon as the fragmentation of hole 1 is completed, blasthole 2 has been destroyed before it is initiated. This phenomenon really happened in practice such as in sublevel caving when two blastholes were close to each other [12]. Therefore, the case Td ≥ Tfs should be avoided. In other words, if Rfg ≥ S, the delay time Td must be shorter than Tfs in order to achieve a successful blasting. 2. Td < Tfs This condition means that before the fragmentation region expands to the second hole, it has been initiated, so the blasting of hole 1 cannot destroy the second hole. A correct delay time should first satisfy this condition. Now we discuss how to determine this condition. Let

Rfg = S = Tfs vfg

(16.8)

where vfg is the expanding speed of the fragmentation region. It is assumed that vfg = Cfgvc. Here vc is the propagation ­velocity of the radial cracks produced by blasting and Cfg is a constant less than 1. These radial cracks will induce branching cracks as they propagate, which is a typical phenomenon under dynamic loading of rock materials [13,14]; see also the chapter: Effect of Loading Rate on Rock Fracture. Thus Eq. 16.8 can be written as S = CfgTfs vc

FIGURE 16.10  Fragmentation region larger than spacing.

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Then we can get



Tfs =

S Cfg vc

(16.9)

Td <

S Cfg vc

(16.10)

Further, Td < Tfs can be changed into



This formula just assures that hole 2 will not be destroyed by the detonation of hole 1, but it does not take the fragmentation result into consideration. To choose a correct delay time for good fragmentation, it is necessary to do the wave analysis under the condition of Rfg < S. In the future, the case Td < Tfs will become more and more common as electronic detonators are widely used and rock fragmentation is to be greatly improved.

16.5  DELAY TIME BETWEEN ADJACENT ROWS For a multirow blast, there are three phenomena that may result: (1) Stress waves from adjacent rows may be superimposed on each other. (2) Fragments produced from neighboring rows may collide with each other during blasting. (3) Neither stress wave superposition nor fragment collision happens. All three phenomena are dependent on the delay time and initiation plan. This is to be discussed in the following.

16.5.1  Stress Wave Superposition After initiation and before the fragmentation from the first row reaches the boreholes in the second row, if the second row is initiated, it is possible that the stress waves from the blasting of both rows may be superimposed together, but the resultant stresses within the rows may be either higher or lower than that caused by one single row, depending on the delay time, the waveforms, charging geometry, velocity of detonation (VOD), and so on. In other words, the delay time should be carefully chosen in order to achieve better fragmentation. Because the delay time between rows and that between holes are similar to each other, the stress wave interaction between rows can be analyzed by using the similar method as in the delay time between blastholes. A longer delay time between rows is usually employed in engineering blasting, compared with the delay time between holes, since it is thought that a longer delay time between rows can make a good free surface and enough space for the next row.

16.5.2  Collision of Fragments We take two cases to discuss: (1) multirow blasting with a delay time in open pit mines or quarries, and (2) production blasting in sublevel caving.

16.5.2.1 Collision Between Fragments From Multirows in Open Pit Blasting Theoretically, if delay time is larger than zero between two neighboring rows and all fragments are thrown toward the same direction, the collision between the fragments from both rows is impossible during their flight, assuming that the fragments from both rows have the same moving speed. However, when the second row is fired, the fragments from this row will strike the muckpile of the first row; that is, a collision is caused. Such a collision is favorable to rock fragmentation. A similar collision will happen for the third and other following rows, too. Even for the first row such a collision is good for fragmentation. But the collision-caused contribution to the fragmentation for the first row is different from the other rows. In open pit blasting, the first row consumes more energy in fragment throw and rotation than other rows since nothing in front of the first row stands and hinders the movement of the fragments. In contrast, the other rows such as the second row take less energy in both throw and rotation because the muckpile that has already been formed by the first row can partly stop further movement of the fragments from the second row, as shown in Fig. 16.11a and b. In this way part of the kinetic and rotation energy saved in the second row will partly be transformed into effective energy to reinforce the rock fragmentation. This is why production blasts in open pit blasts show that the first row often produces poor fragmentation or oversize fragments. It can be inferred that the more rows there are in a blast, the better is the fragmentation in the rows except for the first row. This will be further discussed in the chapter: Rock Blasting in Open Pit Mining.

328 PART | IV  Basic Parameters of Rock Blasting

FIGURE 16.11  Collision of fragments in blasting. (a) Flying fragment from the first row in open pit blasting; (b) muckpile formation of multirow blasting; (c) sublevel caving blasting against an empty room; (d) sublevel caving blasting against fragmented or caved rock.

16.5.2.2 Collision of Fragments in Sublevel Caving For sublevel caving in big and slanting ore bodies, a number of drifts are often driven from the foot wall to the hanging wall in each level, and production blasting starts from the hanging wall. In this case, the first several rings are to be blasted beneath the hanging wall; see Fig. 16.11c. The ore extraction in such a case can be conducted by two methods: (1) After each blast (one or two rings) the ore fragments are completely extracted to form an empty room in front of the ring to be blasted the next time. (2) After each blast, only a small amount of ore fragments is extracted, and the rest will be left. Comparing both methods, one can find that the first method has a lower energy utilization since the fragments produced by blasting can freely fly into the empty room. The flight of the fragments consumes much energy in their rotation and movement, and this is a waste to detonation energy. In contrast, the second method can reduce such energy loss because the remained ore fragments in front of the ring to be blasted hinder the flying fragments; see Fig. 16.11d. Therefore, the kinetic energy carried by the flying fragments can partly be converted into effective energy used to break both the flying fragments and the remained ones again. The second method has another advantage: A seismic event caused by the hanging wall cave may be either reduced in scale or avoided since the big empty room shown in Fig. 16.12c exists no longer. There are other factors such as the initiation plan in a blast which more or less affect the collision of the fragments from neighboring blastholes. We leave this to future study. In summary, the procedure for determining the delay time between blastholes is also valid for the delay time between rows. In open pit or quarry blasts, it is often advisable to choose a much longer delay time between rows than that between holes, but this needs further study. The collision of fragments in both surface and underground blasts is favorable to rock fragmentation. To reinforce this collision, it is better to increase the quantity of rows in one open pit blast. In sublevel caving, this can be done by leaving the fragments from previous blasts so as to avoid an empty room in front of the ring to be blasted.

16.6  SIMULTANEOUS INITIATION IN PRODUCTION BLASTS Simultaneous initiation of multiholes is usually used in smooth and presplit blasting. The basic mechanism of smooth and presplit blasting has been presented in the chapter: Air Deck and Smooth Blasting. In mining and quarry blasting, however, the simultaneous blasting is employed in some mines and quarries, too. Regarding this situation, we will make a qualitative analysis of the simultaneous blasting. We will discuss the case of a complete free surface.

Delay Times Chapter | 16

329

FIGURE 16.12  Stress distribution in the case of complete free surface.

16.6.1  Stress Analysis In order to make analysis simple, we reduce the blasting occurring in three-dimensional condition into a plain strain problem, as shown in Fig. 16.12. The boundaries EG, GH, and HF are completely confined by the same material as the model EFHG, meaning that a stress wave can go through them without any reflection or energy loss. Boundary EF is a free surface. There are two blastholes A and B in the model, and they are initiated instantaneously. Only P-waves from each hole are considered, while S-waves are neglected. As soon as the charges in the holes are initiated, P-waves start to propagate outward. After a certain time, the fronts of the P-waves come to the positions where two circles are located. During this period of time, two tensile stress waves travel into the model from the free surface EF. At the same time, cracks between and outside A and B may start to emerge along line AB due to pure tangential tensile stress. Now let us see the stress distribution at this moment shown in Fig. 16.12. First, all of compressive P-waves are located in the area surrounded by EFJKIE within which the two P-waves from both holes overlap each other in the area MNBKAM. Second, all tensile stresses reflected from the free surface are located in the region EFDLCE, in which the two tensile waves are superimposed in the area MNLM. It can be found that the stress distribution and rock fracture in the simultaneous blasting have the following characteristics: 1. A new fracture surface along line AB will be formed very fast, partly because this surface is a principal surface where tangential stress is principal one and tensile, and partly since the crack extension speed between A and B is much greater than that outside AB according to the experiments [15]; see Fig. 14.9. 2. The radial cracks from either hole will not evenly extend since the whole stress field will be changed as soon as a new fracture surface is initiated at AB. Thus, much energy will be concentrated at the crack tips, giving rise to the faster extension of the crack in AB, while other radial cracks may slow down. 3. As soon as the new fracture surface is produced, the compressive wave from the blasting holes cannot effectively load to the rock over the line AB. This reduces the wave and energy applied to the rock above the AB. As a result, only the waves trapped in this part of the rock can play a limited role in fracturing it. As a result, simultaneous initiation will give rise to a worse rock fragmentation, but it can produce a smooth surface.

16.6.2  Test Results Model blasting experiments in large 15-ton blocks of homogeneous granite, limestone, and sandstone showed that simultaneous detonation resulted in poor rock fragmentation [16]. The result for the multihole blasting indicates that instantaneous initiation in multiholes reduced the crack length in remained rock [17]. Small-scale blasting in concrete blocks indicated that the average sizes of the fragments from simultaneous initiation were greater than those of the fragments from any delayed blasting [8]. A series of small-scale tests in blocks of granodiorite showed that the largest fragments were produced

330 PART | IV  Basic Parameters of Rock Blasting

by the instantaneous initiation [18]. Fractures joining the boreholes were produced, resulting in large fragments. These disappeared as delay increased. At the same time, the point load index (strength) of the fragments is the highest for instantaneous initiation, and then decreases to a low value as delay time is increased. This indicates that in the case of simultaneous initiation, the energy used in cracking or weakening the rock must be much less than that in the case of a delayed blast. Instead, more energy must be used in forming the main crack (which connects the simultaneously initiated boreholes) and in moving the rock fragments. In brief, the experimental and field tests mentioned indicate that the simultaneous initiation with a free surface nearby results in poor fragmentation. This is consistent with the previous stress analysis. Therefore, a simultaneous initiation of two or more blastholes in normal production blasting with a free surface nearby should be forbidden.

16.7  COMMENTS ON DELAY TIME The borehole pressure or detonation wave in a blasthole contains most of the explosive energy. The energy carried with the detonation wave is further transferred to the rock in the form of stress waves. In order to make efficient use of the detonation energy, the stress waves from adjacent blastholes should be efficiently superimposed on each other. In this way, a better stress or energy distribution can be made. Since the original stress wave caused by blasting is a P-wave, a compressive wave with a small tensile tail, the efficient stress wave superposition from adjacent holes should be realized in their compressive parts rather than the tensile ones. For example, an efficient superposition should be the one shown in Fig. 16.3b. All the S-waves, either produced by blasting or reflected from a free surface by a compressive wave, are neglected in this chapter, in order to have a simple analysis. This treatment will influence the result of the determined delay time, but this influence will be limited to a small extent since S-waves are much slower than P-waves. In order to achieve an efficient stress superposition in multihole blasting, the delay time should meet the condition in Eq. 16.7; that is, Td < TP+ + S /cP As described earlier, a zero or very short delay time will give rise to poor fragmentation, so the delay time chosen should not be very small.

16.8  CONCLUDING REMARKS 16.8.1  Reasons for a Delay Time and Factors Affecting Delay Time The reasons for using a delay time in multihole blasts deal with several factors such as ground vibrations, rock damage nearby, seismic events, and rock fragmentation. To determine a correct delay time, the following factors are to be considered: stress distribution, crack propagation, detonation waves, boundary conditions, rock damage nearby, far field vibrations, and movement of fragments.

16.8.2  Delay Time in a Single Hole For a single blasthole, if one detonator is placed in it, no delay time is concerned. In this case, a middle detonator position should be used in an ordinary blast, for example, aiming to achieve good fragmentation. If two or more detonators with the same delay time are placed at different positions in the single hole, a shock wave collision will happen. Such a collision is often favorable to fragmentation. But the detonator position should be correct; especially, a detonation position at or close to the collar must be avoided. Even if a detonator as a backup is planned, it should not be placed at or near the collar.

16.8.3  Stress Distribution and Delay Time Stress distribution plays a dominant role in determining the delay time between two neighboring blastholes, while the other factors are to be checked after the delay time is chosen on the basis of stress distribution. The stress distribution in three-dimensional conditions should be used to determine the delay time, but that in two-dimensional conditions is good enough to use if the detonator positions in all holes are identical. The same principle is valid for the delay time between two neighboring rows, too. As only P-waves are considered but all S-waves are neglected, the ranges of delay times in different cases can be summarized as follows:

Delay Times Chapter | 16

331

l

As the fragmentation radius is smaller than spacing, which dominant current engineering blasting with electric and non-electric detonators, there is not any kind of stress wave superposition from two adjacent blastholes if the following condition (ie, Eq. 16.4) is satisfied: Td ≥ 2TP +

2 S − Rfg cP

.

l

As the fragmentation radius is smaller than spacing, there is an inefficient stress wave superposition from two adjacent blastholes if the following condition (ie, Eq. 16.6) is satisfied: TP+ + S /cP ≤ Td ≤ 2TP + (2 S − Rfg )/cP .

l

As the fragmentation radius is smaller than spacing, there is an efficient stress wave superposition from two adjacent blastholes if the following condition (ie, Eq. 16.7) is met: Td < TP+ + S /cP .

l

As the fragmentation radius is equal to or larger than spacing, and the delay time is smaller than the expanding time of the fragmentation region from one hole to its adjacent neighboring hole, the delay time should first meet the condition in Eq. 16.10, as follows: Td < S /(Cfg vc ).

Then the correct delay time for good fragmentation can be determined on the basis of a detailed stress wave analysis. This case will become common in the future when electronic detonators are dominant in rock blasting.

16.8.4  Simultaneous Blasting Simultaneous initiation of multiholes is necessary for smooth blasting and presplit techniques. Both techniques have been proved to be successful in engineering rock blasting aiming at a smooth surface. However, simultaneous initiation of two or more blastholes in a row or a ring with a free surface nearby should be abandoned in the production blasts in mines or quarries, particularly in the case where the row or ring has a free surface nearby and a large empty space in front of the free face. For example, in sublevel caving a production ring should not employ the simultaneous initiation in two or more blastholes; in open pit blasting this should be also avoided, especially in the first row close to the free face.

16.9 EXERCISES 1. As a delay time is determined, several factors should be considered. Which factor is the most important one? Why? 2. Why is a delay time often applied to a multihole blast? In mining production blasting, if all of the blastholes in a row or a ring are fired at the same time, will the fragmentation be better or worse? Why? 3. As a proper delay time is used between two adjacent blastholes, and the two compressive parts of the two P-waves overlap each other, as shown in Fig. 16.3b, we call this superposition an efficient stress superposition. Which positive results can such an efficient superposition give rise to in production blasting aiming to achieve good fragmentation? 4. If Rfg < S, Ls = 12 m, cP = 5000 m/s, S = 6 m, Rfg = 2.5 m, D = 5000 m/s, and mBP = 4, what is the range of delay time corresponding to each of the following conditions? a. There is not any kind of stress wave superposition. b. There is inefficient stress wave superposition. c. There is efficient wave superposition. 5. As Rfg ≥ S and Td < Tfs, if the condition Td < S/(Cfgvc) is satisfied, should the fragmentation be good? Why? 6. Why does a simultaneous initiation of multiholes never result in good fragmentation in production blasts?

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