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THE EFFECT OF DECOUPLING RATIO ON EXPLOSIVE GENERATED ENERGY RELEASE
Britton, Robert R.
Ohio State University, Ph.D. 1987
© 1987
by Britton, Robert R. All rights reserved.
UMI 300 N. Zeeb Rd. Ann Arbor, MI 48106 PLEASE NOTE:
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University Microfilms International THE EFFECT OF DECOUPLING RATIO ON EXPLOSIVE GENERATED ENERGY RELEASE
DISSERTATION
Presented in P artial Fulfillm ent of the Requirements fo r
the Degree Doctor of Philosophy in the Graduate
School of the Ohio State University
By
Robert R. Britton, B.A., B.S., M.S.
******
The Ohio State University
1987
Dissertation Committee: Approved by
J. S. Gozon
D. R. Skidmore
D, A. Mendelsohn ©1987
ROBERT R. BITTON
All Rights Reserved To George T. and Gladys E. B ritton whose love, patience and understanding have been a constant source of strength and guidance, I dedicate this work.
11 ACKNOWLEDGMENT
The author wishes to thank Dr. Calvin J. Konya for his support and assistance during this project* to Drs. Duane Skidmore, Jozsef
Gozon and Daniel Mendolsohn fo r th e ir interest and suggestions* and to Vishwa Bhushan for his assistance with the testing.
Gratitude 1s also extended to the U. S. Bureau of Mines Research facility at Bruceton, Pa. without whose help this study would never have been possible. Thanks is also due Lennart Clausson, Ray Hunter and T. R. Myers for their technical assistance.
Special thanks 1s extended to Patricia A. Britton who labored long and hard typing this work.
111 September 16, 1933 Born - Wheeling, West Virginia, U.S.A.
1947 - 1979 ...... Worked in industry and private business
1979 - 1987 ...... Graduate Fellow working toward Masters and Doctoral Degrees
1958 ...... Diploma - Machine Shop Practice - ICS
1972 ...... B.A. - Sociology - Univer s ity of South Florida, Tampa
1976 ...... Teaching Certification - West Liberty State College, W.Va., (Ohio and M.Va.)
1 9 8 1 ...... B.S. - Mining Engineering, The Ohio State University
1983 ...... M.S. - Mining Engineering, The Ohio State University
PUBLICATIONS
Britton, R.R., Gozon, J.S., "Some Aspects of Drilling Rig Selection", Proceedings of the Second NMIMT Symposium on Mining Techniques - Mining Equipment Selection, Socorro, New Mexico, (1983).
Gozon, J.S., and Britton, R.R., "Drilling Rig Selection for Small Coal Stripping Operations", Publications of the Technical University for Heavy Industry, Miskolc, Hungary, (1984).
Britton, R.R., Konya, C.J., and Skidmore, D.R., "Primary Mechanism for Breaking Rock with Explosives", Symposium on Rock Mechanics, Chicago (1984). iv Britton, R.R., Gozon, J.S., and Konya, C.J., "Stackers - The Friendly Giants in Reclamation", Symposium on Surface Mine Equipment and Reclamation, Lexington, Kentucky (1983).
Britton, R.R., and Gozon, J.S., "Grapho-Analytlcal Method of Analyzing Bit Life and Replacement", Mining Science and Tech nology, Vol. 1, No. 3, Elsevier, (May, 1984).
Britton, R.R., Skidmore, D.R., and Otuonye, F.O., "Simplified Methodology fo r Calculation of Explosion Temperature and Gas Pressure", Mining Science and Technology, Vol. 1, Elsevier, pp. 299-303, (1984).
Konya, C.J., Britton, R.R., and Lukovlc, S., "Removing Some of the Mystery from Presplit Blasting", The Journal of Explosives Engineering, The Society of Explosives Engineers, Dublin, Ohio May - June, (1984).
Britton, R.R., Gozon, J.S., "The Giants in Rock - Dream or Reality", Proceedings of the 1984 Symposium on Surface Mining, Hydrology, Sedimentologv, and Reclamation, Lexington, Kentucky.
Britton, R.R.. Gozon. J.S., and Myers, T.R., "Computer-Aided Pump Selection for Mine Dewatering", Proceedings of the Second Con ference on the Use of Computers 1n the Coal Industry, Tuscaloosa, Alabama, A pril 15 - 17 (1985).
Konya, C.J., Britton, R.R., and Gozon, J.S., "Explosive Selection - A New Approach", Proceedings of the 11th Conference on Explosives and Blasting Technique, San Diego, California, January 27 (1985).
Britton, R.R., and Gozon, J.S., "Explosive Gas Pressure and Work", International Journal of Mining Engineering, Vol. 2, pp. 351-354, (1984).
Gozon, J .S ., B ritto n , R .R ., and Fodo, J ., "Predetermining Average Fragment Size, A Case Study", International Symposium on the Application of Rock Characterization Techniques In Mine Design, AIME Meeting, New Orleans, March 2-6, 1986.
Britton, R.R., and Gozon, J.S., "Borehole Pressure Correction Equation", International Journal of Mining Engineering, Issue 4.1, March, 1986.
Konya, C .J ., B ritto n , R .R ., and Lukovic, S ., "Charge Decoupling and Its Effect on Energy Release and Transmission fo r One Dynamite and One Water Gel Explosive", Proceedings of the Thirteenth Conference of Explosives and Blasting Technique, Miami, Florida, Society of Explosive Engineers, (1987). v FIELDS OF STUDY
Major Field: Mining Engineering
Studies in Explosives Engineering with Dr. Calvin J. Konya, and Underground Coal Mining with Dr. Jozsef S. Gozon.
vi TABLE OF CONTENTS
ACKNOWLEDGMENTS...... i i i
VITA ...... 1v
LIST OF TABLES...... ix
LIST OF FIGURES...... xi
CHAPTER PAGE
1 INTRODUCTION ...... 1
2 REVIEW OF RELATED LITERATURE ...... 4
2.1 Detonation ...... 4 2.2 Stress Wave ...... 9 2.3 Coupling and Decoupling ...... 13 2.4 Other Decoupling Studies ...... 19 2.5 Detonation Velocity ...... 31 2.6 Underwater Testing ...... 32 2.7 Statistical Model...... 35
3 EXPERIMENTAL PROCEDURE...... 38
3.1 Test Site ...... 38 3.2 Charge P re p a ra tio n ...... 38 3.3 Instrumentation ...... 40 3.4 Test Results...... 43 3 .4.1 Scaled Time Constant...... 45 3.4.2 Scaled Impulse ...... 45 3.4.3 Scaled Peak Shock ...... 45 3 .4 .4 Relative Shock Energy ...... 46 3.4.5 Shock Energy ...... 46 3 .4 .6 R elative Bubble Energy ...... 48 3.4.7 Bubble E n erg y ...... 48 3.4.8 Total Energy ...... 48 3.4.9 Detonation Velocity ...... 49 3.4.10 Comparisons ...... 49
v ii TABLE OF CONTENTS (c o n t'd .)
CHAPTER PAGE
4 DATA ANALYSIS AND CONCLUSIONS...... 51
4.1 Statistical Analysis...... 51 4.2 Relationships Between Shock Energy, Bubble Energy and Decoupling Ratio ...... 66 4 .2 .1 Bubble Energy ...... 66 4.2.2 Shock Energy ...... 70 4 .2 .3 Summary...... 74 4.3 Determine Cause of Energy Loss ...... 74 4.3.1 Detonation Velocity ...... 74 4 .3 .2 Summary...... 80 4.4 Magnitude of Energy Loss Due to Decoupling ...... 81 4.4.1 Total Energy ...... 81 4.4.2 Percent of Total Energy ...... 81 4 .4 .3 Summary...... 85 4.5 Are the Effects Limited to One General Phenomenon?. . 93 4.6 Conclusions...... 4.7 Future Research ...... 95
APPENDICES
A. Preparation of M aterials ...... 97
B. Derivation of Relationships In An Ideal Detonation. . 99
C. Explosive Data ...... 104
D. Detonation Velocity Traces ...... 106
E. Piezoelectric Gage Specifications ...... 115
F. Underwater Measurement Techniques ...... 121
G. Statistical Outputs ...... 152
H. Calculation of Explosion Pressure ...... 167
I. Energy-Breakage Correlation ...... 174
BIBLIOGRAPHY...... 180
v i i i LIST OF TABLES
TABLE PAGE
1. Decoupling Experiments ...... 37
2. Input Data...... 54
3. Scaled Peak Shock - Dynamite ...... 56
4. Shock Energy - Dynam ite ...... 57
5. Bubble Energy - Dynamite ...... 58
6. Total Energy - Dynam ite ...... 59
7. Detonation Velocity - Dynamite ...... 60
8. Scaled Peak Shock - Water G el ...... 61
9. Shock Energy - Water Gel ...... 62
10. Bubble Energy - Water G e l ...... 63
11. Total Energy - Water Gel ...... 64
12. Detonation Velocity - Water G el ...... 65
13. Percent Total Energy ...... 92
14. Similitude Constants for Standard Explosives...... 141
15. Comparison Between Underwater Tests and Rock Tests. . 145
16. Explosive Compositions fo r the Tests ...... 150
17. Measured and Calculated Explosive Energy ...... 151
18. Peak Shock - Water Gel ...... 153
19. Bubble Period - Water G e l ...... 154
20. Root-Mean-Square Value - Shock Pulse - Water Gel. . . 155
ix LIST OF TABLES (c o n t'd .)
TABLE PAGE
21. Shock Loss Factor - Water Gel...... 156
22. R elative Bubble Energy - Water Gel ...... IE'
23. R elative Shock Energy - Water Gel ...... 158
24. Modified Total Energy - Water Gel ...... 159
25. Peak Shock - Dynamite ...... 160
26. Bubble Period - Dynamite ...... 161
27. Root-Mean-Square Value - Shock Pulse - Dynamite. . . . 162
28. Shock Loss Factor - Dynamite ...... 163
29. R elative Bubble Energy - Dynamite ...... 164
30. R elative Shock Energy - Dynamite ...... 165
31. Modified Total Energy - Dynamite ...... 166
32. Breakage - Pressure Correlation Data ...... 176
x LIST OF FIGURES
FIGURES PAGE
1. Reaction Zone in an Explosive of Infinite Extent. . . 5
2. Pattern of Expansion of Explosion Products from a F in ite Bounded Charge in A1r ...... 6
3. Pressure, Temperature, Density, and Composition Distributions Within the Reaction Zone ...... 8
4. Attenuation Zones Surrounding a Cavity Containing an Explosive Charge ...... 11
5. Geometry of a Decoupled Explosive Charge in a Hole. . 16
6. Percent R elative Strain Amplitude Versus Percent Coupling...... 18
7. Composite Plot of R elative Strain or Velocity Amplitude Against Decoupling ...... 20
8. Decoupling Ratio Versus Breakage ...... 22
9. Borehole Pressure Versus Breakage ...... 23
10. Breakage Versus Decoupling Ratio ...... 24
11. Total Broken Rock Versus Decoupling Ratio ...... 26
12. Percent of Maximum Fines Versus Decoupling Ratio. . . 27
13. Percent Reduction of Fines Versus Decoupling Ratio. . 28
14. Breakage Versus Hole Diameter ...... 30
15. The Underwater Explosion Phenomenon ...... 34
16. Test Setup ...... 39
17. Diagram of Charge Assembly ...... 41
xi LIST OF FIGURES (c o n t'd .)
FIGURES PAGE
18. Charge Assembly ...... 42
19. Instrument Setup ...... 42
20. Line Diagram of the Instrumental Setup ...... 44
21. Bubble Energy Versus Decoupling ...R atio...... 67
22. Bubble Energy Versus Decoupling ..R atio...... 68
23. Bubble Energy Versus Decoupling R atio ...... 69
24. Shock Eneray Versus Decoupling Ratio ...... 71
25. Shock Energy Versus Decoupling Ratio ...... 72
26. Shock Energy Versus Decoupling Ratio ...... 73
27. Detonation Velocity Versus Decoupling R atio ...... 75
28. Detonation Velocity Versus Decoupling Ratio ...... 76
29. Detonation Velocity Versus Decoupling Ratio ...... 77
30. Shock Loss Factor Versus Decoupling Ratio...... 79
31. Total Energy Versus Decoupling Ratio ...... 82
32. Total Energy Versus Decoupling Ratio ...... 83
33. Total Energy Versus Decoupling Ratio ...... 84
34. Percent of Total Energy Versus Decoupling Ratio for Water Gel ...... 86
35. Percent of Total Eneray Versus Decoupling Ratio for Water Gel ...... 87
36. Percent of Total Energy Versus Decoupling Ratio for Water Gel ...... 88
37. Percent of Total Energy Versus Decoupling Ratio for Dynamite ...... 89
xi i LIST OF FIGURES (c o n t'd .)
FIGURES PAGE
38. Percent of Total Energy Versus Decoupling Ratio for Dynamite ...... 9C
39. Percent of Total Energy Versus Decoupling Ratio for Dynamite ...... 91
40. Percent Relative Strain Amplitude and Percent Shock Energy fo r Dynamite and Water Gel Versus Decoupling Ratio ...... 96
41. 1.25 Inch Diameter Pipe; TR-2 ...... 107
42. 1.25 Inch Diameter Pipe; TR-2 ...... 107
43. 2.00 Inch Diameter Pipe; TR-2 ...... 108
44. 2.00 Inch Diameter Pipe; TR-2 ...... 108
45. 3.00 Inch Diameter Pipe; TR-2 ...... 109
46. 3.00 Inch Diameter PiDe; TR-2 ...... 109
47. 4.00 Inch Diameter Pipe; TR-2 ...... 110
48. 4.00 Inch Diameter Pipe; TR-2 ...... 110
49. 1 .2 5 .Inch Diameter Pipe; Red-D ...... I l l
50. 1.25 Inch Diameter Pipe; Red-D ...... I l l
51. 2.00 Inch Diameter Pipe; Red-D ...... 112
52. 2.00 Inch Diameter Pipe; Red-D ...... 112
53. 3.00 Inch Diameter Pipe; Red-D ...... 113
54. 3.00 Inch Diameter Pipe; Red-D ...... 113
55. 4.00 Inch Diameter Pipe; Red-D ...... 114
56. 4.00 Inch Diameter Pipe; Red-D ...... 114
57. The Piezoelectric Gage ...... 118
xi 1 1 LIST OF FIGURES (c o n t'd .)
FIGURES PAGE
58. Underwater Shockwave Parameters ...... 123
59. Typical Underwater Test Setup and Results ...... 124
60. Shock Front From a Line Charge ...... 126
61. Effect of Gage Location in Underwater Tests ...... 127
62. Shape Factor fo r Various Charge Shapes ...... 138
63. Shock Loss Factor Vs. Detonation Pressure...... 138
64. Nomogram fo r Shock Wave Parameters fo r TNT ...... 143
65. Nomogram fo r Bubble Parameters fo r T N T ...... 144
66. Typical Strain Wave and Pressure Pulse ...... 145
67. Correlation Between Underwater Tests and Lead Block Tests...... 147
68. Bubble Energy Vs. Calculated Expansion Work ...... 147
69. Impulse Vs. Calculated Expansion Work ...... 148
70. Fragmentation Vs. Calculated Energy ...... 148
71. W% Versus Breakage-Pressure ...... 178
xi v CHAPTER I
INTRODUCTION
The objective of this research project was to determine the cause and extent of energy changes in decoupled boreholes. Decoup ling ratio was defined as the diameter of the borehole divided by the charge diameter.
In situations requiring decoupled charges, such as controlled blasting applications, a knowledge of the effect of explosive energy release is important in pre-determining the condition of the highwall face or road cut a fte r blasting.
There are two types of energy released from a blast--shock energy and gas energy. Charges set off in a borehole produce these types of energies, and it is thought that the shock energy causes the crushing about the borehole and leaves microfractures on the borehole wall, while the gases induce and pervade propagating fractures out into the burden. This gas energy was considered the primary force responsible for the work done by the explosive charge. Consequently, when charges are used in an unconfined s itu a tio n , such as mud capping, the work is presumably accomplished by shock energy because no mech anism is present to contain and thus u t iliz e the gas energy p o ten tial.
Recently conducted research produced data which question the previously held assumptions about the energy loss phenomena that
1 2 occur with decoupling 1n a borehole {21, 69). The original theory indicated that fully coupled charge should generate a greater volume of breakage than those possessing greater decoupling ratios. That is, i t has been accepted theory that decoupled charges produce energy losses across the air gap and therefore transmit less total energy to the rock mass to be broken. I t could be concluded from th is th at as decoupling ratios increase, there would be corresponding energy losses.
Even though decoupled charges are not as e ffic ie n t from the standpoint of blasthole utilization and even though decoupled slurry charges can suffer inefficient detonation due to channel effects, there is s till good reason to explore the conditions produced by decoupling in bore holes since its use is widely practiced.
Tests conducted by B ritton (21) and experiments by Paithanker
(69) contradict the original theory. Both of these studies found, after seiving and sizing the broken material, that maximum fragmen ta tio n was not produced a t a decoupling ra tio of one, but each found maximum values at a decoupling ratio of approximately two. Different materials were used in these tests; therefore, the results should not be characteristic of a particular material. Also, for both the dynamite and the water gel in this study, the detonation velocity was well within the range of the manufacture's rating.
Since decoupling plays such an important role in blasting, this research project was undertaken to try to shed some additional light on the effect of decoupling on total energy release. The primary objective was to: 3
1. Determine the relationship between shock energy and bubble
energy 1n decoupled charges,
2. Determine the magnitude of energy loss as a result of
decoupling,
3. Determine if energy loss is due to the loss of confinement
or due to channel e ffe c ts , and to
4. Determine if these effects are limited to any one general
phenomenon. CHAPTER I I
REVIEW OF RELATED LITERATURE
2.1 DETONATION
Since in an actual explosion the transformation of an explosive into gaseous products is not instantaneous, the detonation is not
ideal because any chemical reaction takes time to go to completion as shown in Figure 1.
Rinehart and Pearson (75) believe th at the surface o f each particle of the explosive is ignited by the high pressure and temper ature that surround it. They also conterrd that explosive particles are heated in te rn a lly following adiabatic compression by the detona tion wave. The temperature rise indicates burning reactions within the p a rtic le . The same compression may resu lt in heating of gas bubbles within the particles and ignition nearby.
Rinehart and Pearson (75) also contend that the region irrmediate-
ly behind the reaction zone has a high temperature and gas pressure which send particles streaming in the direction of the detonation front at a velocity one-fourth that of the detonation velocity.
Figure 2 shows how the explosions form for a bounded charge
detonated in the air. The detonation products move laterally along
AB and BC while creating release waves which move at about three-
fourths the detonation velocity. The detonation front along AC 4 * & ' • * * > *
»
Of n 6
Reaction Undetonated Shock Wave Zone Explosive
Front of Explosion
Chapman- Jouget Point
Detonation Front Unexpanded Detonation Products
Zone o f Interaction Between Detonation Products and A ir
Fig. 2 Pattern o f Expansion of Explosion Products from a F in ite Bounded Charge in A ir (A fte r Rinehart and Pearson (7 5 )). maintains a constant pressure. The area Inside A6C sustains a high pressure until affected by the release waves. The release waves travel about six-tenths the detonation velocity. As the momentum of the detonation products Is transferred to the materials to be broken, the lateral movement of the detonation products 1s slowed by that material. The results of this transfer of momentum is a high-inten- sity stress wave in the material.
Figure 3 shows the distributions of the pressure, temperature, density and composition within the reaction zone. Zeldovich and
Kompaneets (89) believe that maximum pressure is obtained just before the reaction 1s initiated, and then falls just behind the detonation front, reaching a constant value when the reaction 1s completed. The temperature rises abruptly just after initiation, and increases s lig h tly as the reaction proceeds and decreases as the reaction reaches completion. Density varies with pressure.
As energy is transferred from the reaction zone to the detonation front, the sound velocity of the detonation products serve as a con trolling factor. Taylor (83) stated the relationship from the
Chapman-Jouquet condition as:
V = U+c (1) where V = the detonation velocity
U = the particle velocity
c = the velocity of sound in its detonation products
The detonation process is described by the Chapman-Jouquet condition and the laws of conservation of energy, mass, and momentum. Temperature Pressure -J i. Pesr, eprtr, est, and Density, Temperature, Pressure, 3 Fig. I i I I ______I _ Reaction Reaction) Zone oe J Zone ecin oe Afe Zloih and Zeldovich fter (A Zone Reaction opsto Ditiuin wihn the )). 9 (8 Kompaneets ithin w istributions D Composition I
x ! _____ > (J O
Reaction
Zone — X 8 > >
9 2.2 STRESS-WAVE
Pearse (71) proposes that as detonation proceeds along the charge, an expanding stress wave pervades the surrounding material.
The shape of this wave is determined by the velocities of the detona tion and stress waves. In most instances, the detonation velocity is larger than the stress-wave velocity so that waves expand spherically from each p a rtic le . The waves come together to form a wave fro n t which moves through the m aterial. The fro nt is inclined from the longitudinal axis of the charge, as it expands radially from the borehole. This angle is determined by the following:
A (longitudinal stress-wave velocity) (0\ Sln * ------(detonation velocity) ------u )
The stress waves are of two forms. The firs t is the longitudinal wave, which is given by:
=\/3K(l-v)/(p(l+v) (3) where C0 = wave velocity for the longitudinal wave
K = the bulk modulus of the material
v = Poisson's ratio of the material
p = the density of the material
The second is the shear wave given by:
Ct V * T (4) 10 where = wave velo city fo r the shear wave
G = the rigidity modulus of the material
p = the density of the material
The stress wave moving from its origin diminishes due to inter
nal friction and geometry. Because the stress level varies rapidly,
natural resistance of the m aterial promotes wave decay. Geometric
retardation results from the divergence of the wave expanding cylin-
dri cally from the borehole.
Atchison and Duvall (10) contend th at two zones around the
explosive explain the diminishing effect on the stress wave (Figure 4).
The first is the transition zone where cracking, crushing, and plastic
flow occur (nonelastic effects), and the second is the seismic zone, where the wave propagates elastically. Some energy absorption by the material occurs so that propagation is not perfectly elastic.
The analysis assumes that simple power-law decay functions of
the transition and seismic zones can be used to describe effects near
the borehole. That is, the wave is diminished more in the transition
zone than in the seismic zone. The following relationship results:
(5)
a = at(R/Rt )'n (6)
where a = the radial stress in the material
R = the distance from the center of the charge
R = the cavity radius w J 11
Cavity Wall
Source Zone
Transition V Zone
Seismic Zone
i— i
h - * .
Fig, 4 Attenuation Zones Surrounding a Cavity Containing an Explosive Charge (After Atchison and DuVal1 (10)), 12 Rt = the transition zone radius
a = the radial stress in the material at the borehole wall
a = the radial stress at the outer radius of the transition zone
m.n = are constants
Atchison and Duvall (10) found m and n to be 2.16 and 2.03, respect ively for granite-gneiss using a gelatin dynamite.
On the other hand, Duvall and Petkof (40), using five different rock types and ten different explosives, found that the following decay function best described the diminishing effect of the stress wave:
A = Cx"Vax (7) where A = is the amplitude of the stress wave
C = a constant
x = the distance the wave traveled through the rock
a = the absorption constant
m = the cylindrical propagation constant or exponent which they found to be 0.5
Because the detonation is controlled by what Cook (30) calls
"edge effects", the ability of the shock wave to jump the air gap introduced by decoupling is a point of controversy. The next topic is concerned with some of the ram ifications of borehole decoupling. 13 2.3 COUPLING AND DECOUPLING
The characteristic impedance ra tio between explosive and rock affects the explosion-generated stress wave in the rock. The relation ship depends on transfer of the stress wave f-om the explosive or explosively generated gases to the rock. The energy waves interact with the rock. Some waves continue through the rock and some are reflected back through the explosive (50),
Cook (30) states that for perfectly coupled boreholes, the rela tionship between the borehole pressure and the explosive is given by the "impedance mismatch" equation:
Pr = 2Pe/(l+R) (8) where Pr = shock pressure in rock
Pg = explosive pressure
R = relative impedance of rock and explosive
The lateral contact of the explosive with the rock has little effect on the stress wave, for the detonation head does not extend to the explosive-rock interface due to "edge effects". Perfect coupling at the ends of the charge does, however, have a positive influence on the stress wave.
If A equals the ratio of charge diameter to borehole diameter, then the borehole impedance for an A is given by the following equation: 14 R ■ (8ApePb)‘s/p r Vr (9) where R = borehole impedance
(8ApePb) = impedance of explosive
PrVr = impedance of rock
Pe = density of explosive
Pr = density of rock
V = velocity of detonation e J
Vr = velocity of shock wave in rock
= borehole pressure
Nicholls and Duvall (64) formulated the following equation using the laws of momentum, mass, and energy conservation:
Stress in a medium = (1+N) (detonation pressure)/(l+NR) where R is the ratio of characteristic impedance of the explosive to rock, and N is the ratio of the mass in the reflected shock front to the mass in the incident shock front. If the two flows are equal, the N equals one, and the equation reduces to:
Stress in a medium = (2) (detonation pressure)/(l+R) (10)
Nichols and Duvall (64) estimated the value of N to be five for various explosives in salt. If R is less than one, N can be greater than one which allows for a greater ratio of stress than that indicated by the acoustic theory which relates detonation velocity, particle velocity, and sound velocity. 15 Decoupling is defined as the ratio of the hole diameter to the charge diameter. However, Atchison and Duvall (10) used the ra tio of the radius of the charge to that of the hole. They ran tests in limestone and granite to study the amplitude and time of explosion generated strain pulses as a function of the decoupled radii. They found that as the decoupling increased, the strain-pulse in the rock decreased, and they contended th a t the source zone (Figure 5) is the cavity between the charge and the hole wall. In the cavity a pressure pulse is generated that impinges on the hole w a ll.
Pressure in the source zone can be estimated by assuming that the expansion of the gas from the explosive is adiabatic and acts id e a lly giving:
P(irR|L)a = Ph(TrR^L)a (11) where P = the detonation pressure
R = the radius of the charge c
L = the length of the hole
a = the adiabatic exponent = Cp/Cv
P^ = the hole wall pressure
R, = the radius of the hole h
Now, solving for Ph gives:
Ph ■ P(Rh/Rc)'Za (12) where Rf / Rc = D* t ^'e decoupling ra tio 16
Explosive Source Charge Zone
Fig. 5 Geometry of a Decoupled Explosive Charge in a Hole (A fte r Atchison and Duvall (10)). 17
In a later study utilizing the work of Atchison e t.a l., Nichols (63) found that under his test conditions that strain and particle velo city were related by the equation:
(13) where E = strain
v = particle velocity
C = longitutinal propagation velocity
Figure (6) shows relative strain amplitudes for four conditions of decoupling. Here, the amplitudes are presented as percentages of the fully coupled amplitudes versus the percent of decoupling. The relationship appears lin e a r on a log-log plo t having a slope of 1,5.
This implies that strain amplitude is nearly proportional to the coupling ratio. The results show the relative amplitudes to be 72% and 55% of the amplitude from coupled boreholes.
Energy considerations are even worse, says Nichols, because energy is proportional to the square of the strain amplitude. There fore, squaring 72 and 55 we get the relative energies of 50% and 30% compared to the energies of the fully coupled blasts. Thus, the total radial strain energy is given by:
(14) where E s total radial strain energy per unit area. a
C = longitudinal propagation velocity, Percent Relative Strain Amplitude 100 i. Pret eaie tan mltd versus Amplitude Strain Relative Percent 6 Fig. ecn Culn ( t Ncos 63)). 3 (6 Nichols r fte (A Coupling Percent ecn Coupling Percent lp 1.5 Slope 100
18 19 e^, = radial strain,
t = time, and
p * density.
Ea was then scaled by W1^3 and plotted as a function R/W1^3, a The propagation of E, may then be represented by: a
E /W1/3 = K(R/W1 /3 )b (15) d where W = charge weight,
R = borehole center to measuring device (fe e t),
K = strain energy intercept constant, and
b = strain energy decay exponent.
Figure 7 shows a composite of relative strain amplitude versus decoupling presented by Atchison et.al. (10).
2.4 OTHER DECOUPLING STUDIES
The preceeding topics involving decoupling were done when the en.phasis was on shock energy, and gas energy was not given much atten tion . I t was thought th at gas energy rose rapidly under high pressure and high temperature and then subsided rapidly performing no useful work. Since then, several studies have been embarked upon to discover the relavence of gas energy in the process of breaking rock.
That is, if properly confined will the shock energy or the gas energy be the most e ffe c tiv e mechanism fo r doing e ffic ie n t work? RELATIVE STRAIN OR VELOCITY AMPLITUDE 1.0 .08 .04 .10 .01 j .02 06 i. Cmoie lt f ltv Sri or Strain elative R of Plot Composite 7 Fig. 2 eoiy mltd Aant Decoupling Against Amplitude Velocity Afe Acio et. . 10)), 0 (1 l. .a t e Atchison fter (A 4 DECOUPLING 6
8
Slope * -1.5 * Slope 10 Lithonlo Lithonlo ain o Marion uyu a Bucyrus init *■ Winnfietd 20 o
40
60
80
100 20 21 Britton (21) set out in laboratory tests to determine the role of gas pressure in rock breakage. The experiments were conducted in mortar blocks, using bottom detonated PETN charges. The shock wave, time from detonation to burden breakage and the weight of the crater were measured. The borehole pressure was calculated--Appendix H.
Then, the measured data were compared to decoupling.
The results showed that shock energy played a minimum role while breakage, work, and borehole pressure correlated very well with decoupling. Figure 8 shows breakage versus decoupling ratio where it can be seen that at a decoupling ratio of one, breakage was not at its maximum. For the decoupling ratios greater than one, the relation ship was linear. Figure 9 depicts breakage versus borehole pressure, and this was a derivative plot with the data points placed on after the curve was derived. It is clear that the points follow the curve very closely.
Another decoupling experiment was conducted a t the U niversity of
Missouri-Rolla by Warden (86). These tests were conducted in the field in horizontal boreholes using 60% ammonia dynamite having a specific gravity of 1.29 g/cc. He, too, found good correlation between borehole gas pressure and rock breakage, while the role of shock energy was minimal. Although the method of calculating effec tiv e borehole pressure d iffered from B ritto n , the relationship between the crater weight and decoupling was linear when the decoupling ratio of one was ignored. Also, using crater weights of from -3/16 inches to + 6 Inches, it was shown that breakage was not at Its maximum at one but at some decoupling ratio approaching two. See Figure 10. Crater Height (g) 800 600 400 200 — 1.0 i. Dculn Rto versus Ratio Decoupling 8 Fig. 1.5 eopig Ratio Decoupling raae Afe Brto ( )). 1 (2 ritton B fter (A Breakage 2.0 2.5 3.0 22 Breakage (g) 600 800 400 200 0 2 iue . oeoe rsue versus Pressure Borehole 9. Figure oeoe rsue (10^) Pressure Borehole 4 raae Afer itn 21)). 1 (2 ritton B r fte (A Breakage 6 8 10 23 Rock Breakage (lbs.) 2500-1 0 0 0 2 1000 1500 0.0 - - 1.0 iue 0 Bekg versus Breakage 10. Figure eopig Ratio Decoupling eopig Ratio Decoupling 2.0
3.0 4.0 24 25 Paithanker and Mandal (69) found th at fines were a problem as a result of blasting. Tests were run to come up with a solution.
Using decoupled holes, i t was found that maximum breakage oocured at a decoupling ratio of 2.14, and that the amount of fines were great est at a decoupling ratio of one. Of course, as the decoupling ratio continued to be increased, the breakage decreased. Figure 11 shows total rock broken versus decoupling ratio. The point of interest here is that maximum breakage did not occur at a decoupling ratio of one. Figure 12 gives evidence of the relationship between percent of fines versus decoupling ratio, where the fines are greatest at a decoupling ratio of one. Figure 13 depicts the percent reduction 1n fines to decoupling ratio, and it's clear that as the decoupling ratio increases, fines are significantly reduced. It should also be noted that in this study, as well as Britton's tests, large pieces were also reduced, especially in the middle ranges of decoupling ra tio .
Duvall e t .a l. in the USBM R .I. 5356 reported from collected strain data that a wave motion is generated in the rock as a result of charge detonation. The question is whether this wave motion causes breakage--the reflective theory of rock breakage. This theory is antiquated, but of significance is the role gas pressure was assumed to play in the process. It was assumed that a confined charge creates, almost instantaneously, a large quantity of gases in a very short time producing a compressive stress or strain pulse which travels radially outward into the rock at a speed equal to or greater than the speed of sound in the rock. Associated with this strain Total Broken Rock (g) BOO 400 200 600 0.0 - 1.0 iue 1 Ttl rkn ok versus Rock Broken Total 11. Figure eopig Ratio Decoupling eopig Ratio Decoupling 2.0
4.0 26 Percent of Moximum Fines 0 0 1 0 5 . 2.0 0.0 - - 1.0 iue 2 Pret f aiu Fines Maximum of Percent 12. Figure eopig Rotio Decoupling ess eopig Ratio Decoupling versus 3.0
4.0 27 Percent Reduction of Fines - 0 8 - 0 4 0.0 1.0 iue 3 Pret euto o Fines of Reduction Percent 13. Figure eopig Ratio Decoupling ess eopig Ratio Decoupling versus 2.0
4.0 28 29 pulse 1s a tangential tensile strain pulse. These pulses are exem p lifie d by a single short duration compression having a steep ris e time and slower fall time-shock wave.
He also stated that borehole gas pressure acts against the stenrning, compressing 1t and at the same time producing a compressive stress pulse that moves up the stemming column. Due to the loss of heat and increased volume that results from stenrning compaction and crushing of rock about the borehole, the gas pressure decreases rapidly from its peak value.
His conclusions were that the re fle c tio n theory worked; that is , shock energy was the primary mechanism responsible for rock breakage.
Persson e t. a l. (72) conducted slab blasting experiments in granite using a single extended charge. The critical burden for best breakage was maximized a t a borehole diameter approximately twice the charge diameter. At this optimum borehole diameter there exists an upper lim it to the length of throw and in the mass of
broken rock fo r a given burden and charge size.
One of the significant findings of this study was that total weight of removed rock as a function of borehole diameter and burden
produced results similar to Britton (21) and Paithanker (69). Here
the bench height and charge weight were held constant at 1.5m and
0.070 kg/m respectively. Figure 14 shows that for boreholes having
diameters approaching that of the charge diameter breakage was not
as good as when the borehole diameter was twice that of the charge .
diameter. Here, V represents burden. Total Weight Removed Rock (tons) 10 I I I'l I I 1 I I I I "1 T I I I l ' I I I I I 0 - 5 - 0 40 20 0 iue 4 Bekg vru Hl Diameter Hole versus Breakage 14. Figure oe imtr mm) m (m Diameter Hole Atr eso ( )) 2 (7 Persson (Alter I I I 1 I I I | T I ' T T ' I
30 31 J. Burl In Johnson reported in the Bureau of Mines Report of
Investigations 6012 that scabbing was the primary cause of breakage* and that expanding gases were responsible fo r minimal breakage when charges were well confined. Scabbing, as he describes it, is a direct result of shock energy.
2.5 DETONATION VELOCITY
In studying the detonation velocity in decoupled boreholes, it's imperative that one be concerned with channel e ffe c ts . According to
Udy (8 5 ), channel or plasma effects a ffe c t explosive types d if f e r ently. Therefore, explosive choice could be an important factor when using decoupled boreholes.
Udy made a study by exploding charges in pipe. He found that externally generated plasmas, highly ionized zones of reacting material ejected from the surface of detonating charges, are the primary cause of channel e ffe c ts . Furthermore, the dead pressing of an explosive column In a borehole having an air annulus between the explosive and the borehole wall is a direct result of explosive generated plasma. Slurries sensitized with PETN, and the dynamites tested showed no degradation of energy, while slurry formulations did.
In some cases, the explosive did not fail fully, but it did retard the detonation to a lesser degree. By packaging the explosive in a type of material such as paraffin wax impregnated paper, the intensity of the plasma produced was reduced. He also found that placing detonation cord along the length of the charge eliminated plasma effects. 32
Cook (31) also found that channel effects could present a problem in decoupled holes.
2.6 UNDERWATER TESTING
If an explosion, as described by Cole (27), takes place in water, the firs t registered disturbance to the water is the arrival of the shock wave at the water boundary with the explosive {14, 27).
The resu lt is a pressure wave which moves the water outward from the center of the explosion. The pressure rise in the wave is nearly instantaneous, but the decay is exponential. In comparison with an acoustical wave in water, the shock wave displays the following characteristics near the explosion:
1. Its speed is more than 5000 feet per second, which
is the speed of an acoustical wave.
2. The pressure falls faster than the inverse of the
f ir s t law.
3. The wave p ro file broadens with advance.
Upon completion of detonation, a very dense mass of resultant gases expands as a bubble. The water in the imnediate vicinity of the bubble takes on a s ig n ific a n t outward v e lo c ity . With bubble expansion, pressure gradually decreases, but the motion persists because of in e rtia . Compression continues while gas pressure con tinues to fall to a point below the equilibrium value composed of the sum of the hydrostatic and atmospheric pressures. This pressure effect brings the outward flow to a stop, and at this point, the 33 boundary of the bubble begins to contract a t an increasing rate .
The inward motion continues u n til the com pressibility of the high
pressure gases deter and fin a lly , but abruptly, reverse the motion.
Thus, the bubble oscillates several times.
Figure 15 shows these phenomena fo r suspended charges from both the surface and bottom of the water, (1 7 ). The pressure pulses
are emitted from the bubble near its minimum. The dotted curve
represents the position of the bubble center as a function of time.
The bubble has great buoyancy due to the effects of gravity; there
fo re , i t moves upward. This upward motion is rapid with a pulsating
motion. The bubble does not float up slowly.
The items measured were shock energy, bubble energy, re la tiv e
shock energy, relative bubble energy, total energy, modified total
energy and detonation velocity. The items measured which had the
most relavence to this study were relative shock energy, relative
bubble energy, shock energy, bubble energy, total energy and modified
total energy. These variables are dependent upon the interaction of
the explosive type, charge weight and decoupling ratio. As decoup
ling ratio is increased, the energy released from one of the
explosive types give relationships which allow for analytical com
parisons over the range of decoupling ratios. The equations used to
calculate these relationships and the techniques for their measure
ment are found in Appendix F. e r u g i F PRESSURE SHOCKWAVE 15 The Underwater Explosion Phenomenon (AfterRoth (76)) Phenomenon Explosion Underwater The 1ST BUBBLE 1ST PULSE
2NO BUBBLE 2NO PULSE
R BUBBLE 3RD PULSE
TIME 34 35 2.7 STATISTICAL MODEL
This research utilized a factorial experiment of the order
4x2x2. It involved four decoupling ratios, two explosives, and two explosive weights. It provides for sixteen possible combinations; therefore, in the alloted time approximately two of each combination could be expected, perhaps more of one or two combinations. I t so happened that nineteen good shots were made.
The goal was to construct confidence intervals for differences between decoupling ratio s fo r each explosive a t each charge weight.
According to Satyauratan and Vedem (79), a standard deviation of about 5% of the mean is expected in underwater measurements; and i f the standard error is 5% of the mean and each observation is repeated two times, the error lim it can range between - 10% producing an eighty percent confidence level.
This experiment was a three factor fixed effect model for a full factorial test having the standard notation:
Yuki *u + ai+ bj+ ck+
(e rro r) (16) where = 1th response to a combination of the ith level 1J of factor A, jth level of factor B, and the kth level of factor C
a^ = ith effect of A on Y
b. = jth effect of B on Y 0 c^ - kth effect of C on Y
(ab).. = interaction of the 1th level of A and the jth J level of B 36
(ac) = interaction of the ith level of A and the kth 1K level of C
(be),. = interaction of the jth level of B and the kth 3 level of C
(abc)4iL. = interaction of the ith level of A, jth level 3 of B and the kth level of C
u = overall average response
For this study, factor A represents the four decoupling ratios
(1, 1.6, 2.4, 3.2), B identifies the two explosives (water gel, dynamite), and C refers to the charge weight {1.209, 1.364). The measured responses Y are scaled peak shock energy (PS), shock energy per unit weight (SE), bubble energy per unit weight (BE), total energy per unit weight (TE), and detonation velocity (VEL) as shown in Table 1. An experimental unit consists of the time required for one measurement. The sequence of comparing each combination was selected at random.
The comparisons of in te re s t are:
I = Y Y 111 112
II = Y Y 111 113
= Y Y III 112 113
IV = Y Y 211 212
V = Y Y 211 213
VI = Y Y 212 213 Table 1 - Decoupling Experiments
10:15 TUESOSI, JUIT 1, 1*15
t t r 01* NT PB Tfi 1 f t TC T ME1 665. KU PS
TNT 3.5 2.500 16BN.3 2# 3.9 4 109.0 5# 5.0 17.130 *67.12 2.0* 12*0.93 I XT 3.5 2.5 00 it##.: 2# 7.5 • 91.5 *57.5 16.670 *91.75 2.0* 12*0.93 T i t 1.25 1 .30$ 1077.9 177.9 157## 112.0 566.0 9.666 310.12 1.67 1011.62 TII 1 .25 1 .209 1077.9 177,0 12 356 106.0 550.0 10.*60 311.9* t.«0 1011.62 I t l 1.25 1 .209 1111.6 161.7 1 3605 112.0 560.D 10.750 325.56 1.55 10*3.95 TII 1 .25 1 .209 1077.9 162.3 15660 112.0 560.0 11 .660 325.00 1.66 1011.62 T Ii 2. 00 1 .209 1027.# 166.7 15200 166.0 630.0 13.300 239.19 1.65 9 6 *.*2 TII 3.00 1 .209 791 .b 19#.2 12619 92.0 #60.0 10.520 292.69 1.#5 7*3.07 T II 3.00 1 .209 511 .6 161.9 • * * .0 220.0 3 .670 207.31 1 .*0 *6 0.2 * m 3.00 1 .209 536.9 19U.1 1 0# 6 7 92.5 #62.5 10.0*0 2*3.06 1 .*0 505.66 T II 3.00 1.209 7# 1 .1 165.0 13619 52.0 260.0 5.916 265.19 1 .55 695.67 T II # .oo 1 .309 606.3 175.0 1 3736 37.5 167.5 2.656 223.60 1.55 569.13 III U. 00 1 .209 690.5 113.# 1 39# 0 53.0 265.0 « .3«3 217,60 1.55 6*6.17 RD 1 .25 1 .36# 1212.6 166.0 1 6696 93.5 *67.5 10.070 351.69 1.76 1093.90 SO 1.25 1 .3 m 1162.1 160.5 20632 96.5 #92.5 12.100 356.69 1.65 10*7.67 RD 2.00 1.360 11# 5.3 169.5 16*51 71.5 357.5 10.300 372.9# 1.76 1032.72 SO 2.00 1 .36* 075.6 20 2.0 17621 99.5 #97.5 11.690 330.9# 1.75 769.71 RD 3.00 1 .36# 555.6 193.0 1 7536 66.5 3N2.S 7 .31* 250.12 1.75 501.17 RD 3.00 1 .36# 536.9 201 .0 16326 110.5 552.5 11 .160 227,56 1.7* *65.93 RD S. 00 1 .36# 6# 0.0 162.0 16116 57.0 265.0 #.297 21B.TS 1 .75 577.09 RD S. 00 1 .36# 102(1.0 163.5 17396 96.5 *92.5 6.610 170.61 1.75 923.3* SO ED OPEN 0.906 . 16#. 0 m 4 a 4 4
HOED OPEN 0.906 7 7 u .7 193.0 4 69.6 390.* 7.957 260.19 • 600.62 «0ED OPEN 1.359 . 169.3 .* * DEB 1.25 1 .359 ) « 3 . i 1 6 « • 0 * 136.0 566.6 9.967 162.61 4 310.20 ROES 2.00 1 .359 ■ 172.7 • . * * 4 4 •
RBE SIC I 51 USE 8E 5E TE HTE 0.97603 60.31* 0.160316 0.097690 0.516053 *57.601 *01.207 901.960 779.122 1.02197 67.420 0.175*7* 0.095261 0.*619*9 *76.376 373.2*6 694.202 760.679 0.76*79 105.135 0.10367* 0.091526 0. *90355 367.35* 310.679 ■712.1** 666.996 0.7729# 101.360 0.110105 0.097019 0.*62103 361.607 256.231 •6*6.9*0 656.450 0.63617 105.135 0.113156 0.099709 0.53*669 391.*01 314.615 7*1.317 717. *96 0 .6 ***6 105.135 0.122737 0.1061#9 0.532631 395.291 335.765 767.630 72D.62* 0.90711 155.62* 0.1*0000 0.123361 0**27759 #2# .61D 267.9*5 727.183 693.101 1.02066 66.360 0.110737 0.097576 0.35*96* *77.665 195.*07 706.935 709.232 b . 63693 *1 .303 0.036632 0.03*0*0 0.065172 392.695 *5.268 #59.661 *67.162 ..01931 66.630 0.10566* 0.093123 0.2*6135 *77.127 1 JO. 617 638. 3*1 6*7.*69 0.66256 *8.612 0.06227# 0.05*672 0.190*92 • 13.11 ( 112.091 551.#68 5*7.955 0.7*70# 35.201 0.03006* 0.026509 0.06# 59 7 3*9 .660 #9.760 # 1 9. « 3 3 *20.693 C.72673 *9.751 0.0*5716 0.0*0262 0.113239 3*0.177 66.633 *27.150 *26.761 0.56515 6#.310 0.106000 0.066165 0.#61666 260.5*1 306.076 601.670 5*1 .121 0.72656 66.616 0.127366 0.103556 0.505931 3*0.095 355.326 730.192 6 * 6 .6D2 0.6*075 6*.<72 0.106*21 0.0661 S3, 0.397009 393.5*7 265.263 691.751 6*2.701 1.0163* 69.720 0.125156 0.101761 0■# 350*9 *76.676 269.026 603.969 752.799 0.86620 61.767 0.076969 0.062597 0.171062 *15.758 113.659 555.669 539.907 1.00329 99.639 0.117*7* 0.095513 0.226*39 *69.632 150.696 bSI.556 629.573 0 . 7u*63 51.397 0.0# 5232 0.036776 0.106690 3*6.6*5 72.3U2 **2.036 *33.391 0.76339 66.616 0.069579 0.05bS72 D . l 1*731 357.336 76.222 *55.236 ##5.9*6 1.13672 ,. 4 • 5*2.366 4 .. 1 . 33721 92.597 0.063758 0.069*56 0.317705 625.932 • 6*6.516 0.6*116 •.. * 393.7*6 . . 0.772*8 12#.566 0.10*916 0.065512 0.157636 361.591 ■ 4 *7*.519 0.63672 . • 4 4 298.979 4 • 4 CHAPTER I I I
EXPERIMENTAL PROCEDURE
3.1 TEST SITE
Tests were conducted at the Pittsburgh Research Center of the
U.S. Bureau of Mines, Department of the Interior, in Bruceton, Pa.
Charges were detonated in a 200 foot diameter pond, which was 27 feet deep near the center. The charges were suspended near the center of the pond from a wire rope which stretched across the pond. The explo sives were lowered to a depth of 12 fe e t beneath the w ater's surface.
A piezoelectric gage was also suspended 12 feet beneath the water surface 12 feet away from the charge. Firing and signal cables ran along the rope from the center of the pond to an instrumentation trailer on shore. Figure 16 shows the experimental arrangement.
3.2 CHARGE PREPARATION
The charges were fire d in 2 foot long by I V 2, 3 and 4 inch diameter steel pipes 1/8, 1/8, 3/16 and h inches thick respectively.
The pipes were threaded on both ends to receive pipe caps each having a 5/16" hole to accomrodate in it ia t o r , velo city probe and make switch wires. Three IV by 8" sticks of explosive were used in each shot.
The sticks were attached to a 5/16" diameter dowel rod for rigidity.
38 39
T ra ile r
»>\ \ V* W '
Water Surface Pressure Gage _
Make Explosive Switch Charge
Fig. 16 Test Setup A spacer at each end of the charge centered the charge within the 40 pipe. The charges were detonated by a cap at the bottom of the
charge column. The pipes with the charges were sealed in water
tig h t bags. The velo city probe was placed along side the dowel rod for protection. Figures 17 and 18 show details.
A make switch connected to the charge triggered the oscilloscope for measurement of the bubble duration, and for the pulse initiation composed of detonation velocity measurement. Another switch stopped
the pulse.
3.3 INSTRUMENTATION
A PCB Piezotronics Inc. underwater blast gage Model 138A05
piezoelectric transducer was used 1n these experiments. The trans ducer is a quarter inch diameter tourmaline crystal inside a plastic tube filled with silicone oil. The crystal is connected to an ICP amplifier within the tube. Operating power for the amplifier and the output signal are conducted over a single conductor coaxial cable with a shield serving as the signal return. A constant current source of 2A to 2mA was applied. Power was provided by an +18 to
+24 volts DC power supply acting through a current regulating diode.
The power supply—Model 438A02 from PCB Piezotronics—was used,
outputting 4 mA at 22 VDC. The gage responded to changes in pressure
and had a sensitivity of 0.95 mV/psi, Effective pressure measurement
ranged to 5000 psl at about a 5 volt output. Details of the trans
ducer are shown in Appendix E. 41
Spacer
— Velocity Probe
Dowel Rod
Explosive Charge
t-n -l — Cap
Figure 17. Diagram of Charge Assembly Figure 18 Charge Assembly Figure 19 Instrument Setup 43 Two Model 2090 Nicolet digital storage oscilloscopes were used to record the shock and bubble pulses which were converted to electrical signals by the gage. The oscilloscope sampled signals at rates up to 10 million points per second. Total memory was 2k bytes per channel. Each channel could be subdivided further into halves of lk byte each. Ten to ninety percent of the memory was available for storage of pre-trigger data. A b u ilt-in disk drive on the scope made permanent records of the data for further anaylsis. Hard copies of the shock and bubble pulses were printed on a Model 7035B Hewlett
Packard xy recorder which was connected to the oscilloscope.
A Model 7D20 Tektronix oscilloscope was the third scope used to record the velocity pulses. A Polaroid camera photographed the velocity pulses. Figure 19 shows the instruments 1n the tr a ile r , and
Figure 20 shows the line diagram for the instrumentation.
3.4 TEST RESULTS
Thirty shots were fired in a ll. Two used TNT and four employed
40% dynamite. The dynamite did not function satisfactorily. I t was replaced with Austin Red D, a permissible dynamite, and eight usable shots were made with that explosive. Eleven shots utilized Dupont
TR-2, a permissible water gel.
The TR-2 shots are described below:
Decoupling Pipe Charge Ratio Diameter (inches) Diameter (inches)
1.0 1.250 1.250 1.6 2.000 1.250 2.4 3.000 1.250 3.2 4.000 1.250 TektronU D.S.O. for DETH Velocity
CRT PCB Pletotronks 483 AO? Constant Current Source CHI :hz
CRTCRT
/ Hkolet 2090 / Hkolet 2090 Digital Stonge Oscilloscope 'Digital Storage Oscilloscope ______for Bubble Period for Shock Pulse Hate Switch H PCB Pleiotrofik* 13BA0S U/W Blast Transducer
Figure 20 - Line Diagram of the Instrumental Setup 45 Pictures of the detonation pulses and the data sheets of the two explosives are found in Appendicies D and C respectively.
The results used the SAS statistical package on the AMDAHL computer at The Ohio State University. The items calculated were: scaled time constant, scaled impulse, scaled peak shock pressure, relative shock energy, shock energy, relative bubble energy, bubble energy, total energy, modified total energy and detonation velocity.
3.4.1 Scaled time constant: The time constant is the time of decay from Pm to Pm/e for shock pressure. The value is obtained from the shock pulse. The scaled time constant, 0$, was calculated by dividing time constant, 0, by the cube root of the charge weight.
(ms/lb ) (17)
3.4.2 Scaled impulse: The total impulse is given by the value of
/ P dt over the duration of the shock pulse in psi-sec. In order to evaluate total impulse, the area under the shock pulse was calculated using the Nicolet 4094 oscilloscope and a XF94 dual disk drive. An
"area" program on the scope calculated / V dt in volts-sec. The value of / V dt was divided by the gage factor 0.95 mv/psi to obtain total impulse, I, in psi-sec. The scaled impulse became:
!s = l° t P dt/W2/3 ( 18)
3.4.3 Scaled peak shock: Peak voltage shown on the shock trace was divided by the gage calibration factor 0.95 mV/psi to yield peak shock pressure, Pn, in psi. The value for peak shock pressure was 46 divided by the cube root of charge weight to yield the scaled peak
pressure given by:
Ps * P„/ W1/3,(psi/lb1/3) (19 )
3.4.4 Relative Shock Energy: Explosive shock energy is propor- 2 2 tional to / p dt. To evaluate / p dt. the root mean square, RMS,
value of the shock pulse was calculateo on the Nicolet 4094 oscilloscope. The RMS value of an electrical pulse is given by:
RMS = (/* V2 dt/t)\ (volts) (20)
That implies that:
V2 dt = (RMS)2t , (volts2/s e c .) (21)
The value of f V2 dt was divided by (0.95)2 to yield f P2 dt. The relative shock energy, RSE, is a ratio of shock energies for the test explosives to that for TNT. RSE was calculated as follows:
2 RSE = ( / P dt/W) test explosive ^ 2 ) ( / dt/W) TNT
3.4.5 Shock energy: Shock energy, SE, measured at distance, R, from the charge is given as:
SE = (4 R2/P0Cq) /J P2 dt (23) where PQ is the density of water (lg/cc) and CQ is sound velocity in 47 water (5000 ft/s ). A loss of shock energy occurs close to the charge.
The loss is not included in the measured shock pulse. This loss is directly related to the detonation pressure, P^, which in turn is related to the detonation velocity, D, and the density of the explosive pe by the equation:
Pd = 0 .2 5 pe D2 (24)
Bjarnholt and Holmberg (16) gave a calibration curve, for the shock loss factor, y, i f Pd is known. Detonation velocity was measured for all shots; therefore, and thus y could be evaluated for each shot. The shock energy ih calories per gram was calculated using:
SE = 3.7314y / P2 dt/W, (cal/g) (25)
2 2 where / P dt is in (psi) /sec. and W is in lbs.
The piezoelectric gage specification required that the output under static pressure should be zero. However, a DC offset of -250 to +250 mV was observed on most of the shock pulses recorded. To compensate for this affect, the base line was defined at the level of the DC offset rather than zero volts for evaluating shock parameters.
The time period for integration of the shock pulse was somewhat arbitrary. Cole, (27) recommended t = 6.70; Roth, (75) suggested t = 50; DuPont used t = 1% of bubble period; and IDL integrated over a fu ll 1 ms. Here, the duration of the shock pulse varied from 300 48 to 400 microseconds, while the time constant remained between 50 and
110 microseconds. The shock pulse was integrated over the entire duration of each record.
3.4.6 Relative bubble energy; Bubble energy, BE, of an explosive is proportional to the cube of the period of bubble oscillation.
Relative bubble energy, RBE, is the ratio of bubble energies of test explosives and to that for TNT. RBE was calculated as follows:
3 (T /W), test explosive RBE = 7 Z 3 (26) (V/W), TNT
3.4.7 Bubble energy: Bubble energy, BE, was obtained from the
W illis (27) formula:
BE = (0.675 T (27) u u where PQ is the static pressure on the explosive which is equal to atmospheric pressure (normally equivalent to 33.95 feet of water) plus the hydrostatic pressure. The bubble energy in calories per gram was calculated using the following equation (for 12 f t . depth of water and 33.95 f t . atmospheric pressure):
BE = 0.78883 x 10-4 x T3/W, (cal/g) (28) where T is in ms and W is in lbs.
3.4.8 Total energy: Total energy released by the explosive was calculated in two ways. The Swedish method made total energy the sum of the SE and the BE if the charge is spherical in shape. For 49 cylindrical shapes, the sum of SE and BE must be multiplied by a
shape factor. Here the shape factor was 1.05, (18). Therefore, the
equation became:
TE = 1.05 (SE + BE), (cal/g) (29)
The other method is the modified total energy, MTE. This method
requires that the RSE and the RBE for each shotbe multiplied by
values for TNT - 560 and 500 cal/g, respectively. Thus, the equation
for MTE is given as:
MTE = 560 RSE + 500 RBE, (cal/g) (30)
3.4.9 Detonation velocity: For electric cap in itia tio n , detonation velocity was determined by dividing the distance between switches by the time between start and stop pulses taken from the oscilloscope.
Measured and calculated values of a ll parameters are shown in
Table 1.
3.4.10 Comparisons: Cole states that for TNT, the following equations are preferable:
Pm = 2.16 x 104 (W1/3/R )1*13 (31) and
T = 4.36 x 103 (W1/3/(d + 33)5/6) (32) where Wis in lb s ., R is in f t . , and d is charge depth in feet. In this study, R = 12 feet, d = 12 feet, and W =2.5 lbs. of TNT. 50
Therefore :
Pm = 2.16 x 104 (2.51/3/12)1*13 = 1839.6 psi (33) and
T = 4.36 x 103 {(2.5)1/3/(12+33)5/6) = 2.480 ms (34)
Measured values of P were 1684.2 and 1684.2- and the measured m values for I were 243.9 and 247.5. Therefore, the measured results were within reason. The data from these experiments are contained in Table 1. CHAPTER IV
DATA ANALYSIS AND CONCLUSIONS
4.1 STATISTICAL ANALYSIS
The following model was used for data analysis using the SAS
General Linear Models Procedure (PROC GLM), (78):
Yijk l = U + D/Ri + EXPj + ^ k + D/R * EXP1j + D/R * ^ i k
+ EXP * WTjk + DR * EXP * WT1jk + Erro r^ ^ (35) where i = 1 means decoupling ratio
i = 1.6 means decoupling ratio
i = 2.4 means decoupling ratio
i = 3.2 means decoupling ratio
j = 1 means TR-2 water gel (TVX)
j = 2 means Red-D dynamite (RD)
k = 1.209 means weight of TR-2 (WT)
k = 1.364 means weight of Red-D {WT)
The model was used to analyze the following response variables:
1. Scaled peak shock pressure, PS
2. Relative shock energy, SE
3. Relative bubble energy, BE
4. Total energy, TE
51 5. Detonation velocity, VEL
The following test hypotheses were carried out:
1. u° . D/R * EXP * all equal mabc *
H1 • D/R * EXP * not a ll equal ABC'
2. H° . D/R * all equal HAB ' EXPij
H1 ■ D/R * not all equal HAB ' EXPij
3. u° . D/R * all equal hac ■ ^ i k
D/R * not all equal hac : ^ i k
4. H° ■ EXP * all equal hbc • ^ j k
EXP * WT.. not all equal hbc : Jk
5. D/R1 = d/ r2 = D/R H? : 3 ■ ° ' R4
D/R not all equal HI ■
6. H° : EXPj = exp2
EXPX = exp2 hb :
7. WTj = wt2 Hc :
WTj = m t2 Hc :
The procedure gives two measures of the effect being tested in each hypothesis, I.e . Type I SS measures the contribution of the effect being tested as each term is added to the model sequentially.
Type I SS may be altered by changing the order of the variables inputed. Type I I I SS measures the additional contribution of the effect being tested when all other effects are persent when the addition is made. This type was used to determine i f an null 53 hypothesis is acceptable. I f PR is greater than F, it's probable that a null hypothesis was rejected even if correct; that is, the level of significance is determined. The significance level for this experiment was fixed at ten percent. This implies that i f an effect
1s reported as significant, the probability that it influences a response variable is less than ten percent. In a ll these comparisons,
Type I I I SS responses were rejected or they were fu lly determined in the Type I SS responses.
After all the trials were run, the results showed clearly that decoupling was the major significant variable and that explosive type and weight had l i t t l e or no effect on overall performance. There were significant responses to decoupling versus peak shock (PH),
Root-Mean-Square Value of Shock Pulse (RMS), Scaled Peak Shock (PS), relative shock energy (RSE), shock energy (SE), total energy (TE), and modified total energy (MTE). The results are shown in Tables 3 to 7 for dynamite and Tables 8 to 12 for water gel. Table 2 displays the source of the input data for the program. The results of other comparisons are found in Appendix G.
Tables 3 and 8 show definite significance between decoupling ratio and peak shock for both explosives. Tables 4 and 9 te ll that there exists a very strong response on shock energy by decoupling.
Tables 5 and 10 say that the only significant relationship is decoupling ratio versus bubble energy. I t also te lls one that PR>F is relatively high so that the effect of decoupling ratio is minimal. Table 2 Input Data
5>RUNf 13:228 AT IJR DAV, MAY2. 1987 OPS EXP DR WT PM TP VEL ■ RMS MU PS
1 TUX 1.0 1 .209 1077,9 177,9 1.5744 310. 12 1 .67 1011.32 2 TUX 1.0 1.209 1077. 9 182.3 15660 325.00 1,66 1011.32 3 TUX 1.6 1.209 1027.4 1 86.7 1 5200 239.19 1 .65 964.42 4 TUX 1.6 1 .209 791, 6 194.2 12619 292.69 t .45 743.07 5 TUX 2.4 1 .209 538. 9 1 94,1 10473 243.06 1 .40 505.36 6 TUX 2.4 1 .209 741. .1 185.0 13819 235.19 1 .55 695.67
7 TUX 3.2 1 .209 606. 3 175.0 13736 223,80 J. I 4.1 4. J 569.13 rr 8 TUX 3.2 1.209 690. .J 173.4 13940 217,80 1.55 643.17 9 Fill 1.0 1.364 1212. 6 166.0 13898 351,69 1.76 1093.40 10 Fill 1.0 1.364 1162.1 130.5 20832 358.69 1.35 1047.37 11 Till 1.6 1 .364 1145.*** 139.5 13451 372.94 1 .76 1032.72 12 RD 1.6 1 .364 875. 8 202.0 17621 330.94 1 .75 739.71 13 RD 2.4 1.364 555.8 193.0 17533 250.12 1,75 501 .17 1A RD 2.4 1 * 364 538 • 9 201 .0 16326 227.56 1 .74 485.93 15 RD 3.2 1 .364 640.0 132.0 18118 213.75 1 ,75 577.09 16 RD 3.2 1.364 1024.0 133.5 17396 170.81 1 .75 923.34
EXP = Explosive VEL = Detonation Velocity in f/s DR = Decoupling Ratio RMS = Root Mean Square Value of Shock Pulse in Volts WT = Weight of Explosive in lbs. MU = Shock Loss Factor . . . PM = Peak Shock Pressure in psi PS = Scaled Peak Shock in psi/lb TB = Bubble Period in ms Table 2 cont'd.
DBS RBE RSE BE SE TE MTE
1 0,73479 0.490355 367.354 310.079 712.144 666.996 ’ 2 0.04443 0.532831 395.291 335.7R5 767,630 720,624 3 0.90711 0.427759 424,610 267.945 727.103 693.101 4 1.02080 0.354984 477.865 195,407 70A,935 709.232 5 1.01931 0.246135 477.127 130.017 630,341 647.439 6 0.33256 0.190492 413.116 112.091 551.460 547.955 7 0.74704 0.034597 349,680 49,780 419.433 420.393 8 0.72673 0.113239 340.177 66, 633 427.150 426.731 9 0.56515 0.461680 264.541 300.470 601.670 541.121 10 0.72656 0,505931 340.095 355.326 730.192 646.602 11 0.84075 0,397009 393.547 26?'. 263 691.751 642.701 12 1.01834 0.435049 476.676 209.020 003.939 752.799 13 0.00820 0.171032 415.758 113.AS? 555.039 539.907 14 1.00329 0.228439 469.632 150.090 651.556 629.573 15 0,74433 0.103890 348.645 ^2.342 442.036 433.391 16 0.76339 0.114731 257.336 7A.222 455.236 445.946
RSE = Relative Shock Energy in cal/g RBE = Relative Bubble Energy in cal/g BE = Bubble Energy in cal/g SE = Shock Energy in cal/g TE - Total Energy in cal/g MTE - Modified Total Energy in cal/g
tn tn Table 3 - Scaled Peak Shock - Dynamite
EXP F: I'
HUMBER f IF nriSEEUATIUMS IN DATA BET - 8 1.4 1 05 SATURDAY, MAY 7 r GENERAL LINEAR MODI I..S PROCEDURE DEPENDENT VARIABLE! PS SOURCE nr BUM nr SOUARES HE AM SQUARE r t'Ai nr MODEL 1 .1 00891, 18459704 1.80891 ,18459904 3.97 ERROR A 273409.2881954A 455A8.71469924 p r •• r CORRECTED TOTAL 7 454300,47778750 0.0934 R-SQUARE C.U. ROOT MSE PS MEAN 0,398175 26,4715 213,46717791 806.40375000 SOURCE DF TYPE T SS E. UAM.IF PR > F
EXP 0 0.00000000 * * DR 1 180891,18459204 3,97 0.0934
WT 0 0.00000000 * 4
DR#EXP 0 0.00000000 4 ♦
UT*EXP 0 0,00000000 1 4
DR*UT 0 0.00000000 * 4
DR#UT#EXP 0 0.00000000 * 1 SOURCE DF TYPE I I I SS F UAL LIE PR > F
EXP 0 0. 00000(100 * 4
DR 0 0.00000000 * *
WT 0 0.00000000 4 t
DR*EXP 0 0 . 0 0 0 0 0 0 0 0 4 ♦
WT#EXP 0 0.00000000 * 4
DR*UT 0 0 . 0 0 0 0 0 0 0 0 * 4
DR#UT*EXP 0 0 . 0 0 0 0 0 0 0 0 4 4 ♦ « 00000000*0 0 dxu*dM*aa * * 00000000*0 0 'd/naa + * 00000000*0 0 dX3*dP1 ♦ * 00000000*0 0 dX3*ya ♦ » 00000000*0 0 i n * * 00000000*0 0 an * ♦ 00000000*0 0 dX3 u < au union u SS I I I UdAd ua uoanos * « 00000000*0 0 dxu*dn*aa ♦ » 00000000*0 0 ift*aa 4 + 00000000*0 0 dX3#dfl * * 00000000*0 0 dxu*aa * ♦ 00000000*0 0 dn [000*0 trfi‘ 601 EB8BATT9* ITStra I ya * ♦ 00000000*0 0 dXU u < .'.id union u SS I UdAl ua uaanos ooooocodi’ Eoc S£Z6Z&LL'LZ 6ti:9*ST £\?ZB\r6, 0 NOUW US USW dUUd *n*u syynos-a ( 000*0 OOHaHtr*Ot'V6S L lydtid auduuddo:) J < dd SSd£fd9fr*1 / / dTSdadoirssvt' 9 yOddU £tJSU6i 19 M TCtrQ S00U6[ [9* i [OkO T iHaow un ion u udontjs NOUW suuvnus uo mis ua uidnos us :u‘invi>jon iMuaNUdua udiuiujudj s u u u n avuNi i ivdunus 'l: aoii ■ Aondnios so: -1t u -- dus oiori ru swuidvndusau ut;i duawnn
uy i jx j
a^LLUBUyfQ - yf6j9U3 ^ooqs - ^ 3LQ6i Table 5 - Bubble Energy - Dynamite
EXP i rri
NUMBER DF OBSERVATIONS tn data f*ft = o 14J05 SATURDAY, MAY 2• 1907 49 GENERAL LINEAR MODELS PROCEDURE DEPENDENT VARIABLEJ BE SOURCE DF SUM OF SQUARES MEAN SQUARE F VALUE MODEL 1 70.58*89314 70.58*8931 1 0*01 ERROR 6 49044,2442943* B174.04071573 PR > F CORRECTED TOTAL 7 491.14.031 10750 0,9290 R-SRUARE C*V. ROOT HSF BE MEAN 0,001-137 24.3039 90.41040159 370,77875000 SOURCE DF TYPE I SS F VALUE PR > F EXP 0 0,00000000 • « DR i 70 * 50*89314 0.01 0.9790 WT 0 0.00000000 * » DR*EXP 0 0,00000000 4 ♦
UT*EXP 0 0.00000000 t •
DR*WT 0 0,00000000 4 4
DR*WT*EXP 0 0 . 0 0 0 0 0 0 0 0 » * SOURCE DF TYPE III SS F VALUE PR > F
EXP 0 0 . 0 0 0 0 0 0 0 0 • 4 DR 0 0 . 0 0 0 0 0 0 0 0 4 4 WT 0 0.00000000 * 4 DR*EXP 0 0 . 0 0 0 0 0 0 0 0 4 4 UT*EXP 0 0 . 0 0 0 0 0 0 0 0 4 * DRKWT 0 0 . 0 0 0 0 0 0 0 0 4 4 DR*WT*EXP 0 0,00000000 * 4 at 00 CT> in
ft » OOOOOOOO'O 0 dX3#in*aa ft * 00000000*0 0 in * an ft ft 00000000*0 0 dX3*lfl ft ft 00000000*0 0 dX3#ya ft ft 00000000*0 0 in • ft 00000000*0 0 30 ft ft 00000000*0 0 3X3 j < ad on "if a 3 SS III 3dAl 3H 333005 « « 00000000*0 0 3X3*in*3a « « 00000000*0 0 10*30 « « 00000000*0 0 dX3*lM « * 00000000*0 0 dX3*3G « * 00000000*0 0 in 6££0*0 cO * 6 OOOOldUd* t££6? 1 30 4 • 00000000*0 0 3X3 3 dd 3D If A 3 SS 1 33A1 3II 333005 00C'£G6£'3*V E9 - ojiivoicyva tr£T£*VT £U009*0 N03N 31 35 W 1003 * A * 3 330005-3 6£do*o dOt-IWOO'dOCCX! L 10101 031333303 j < ad ZLLZZZQZ' l l ' l L 6d9dtr61d*££09tr 9 30333 cO *6 IJOdd l£U£* HcdV 00d81£0£*[££6V I 13Q0M dll If A J 33fllOS Of JO 33301133 30 WHS an 333005 31 :31UfI3fA lN3HN3d3iI J30UJJU3d 01300W 3V3NI1 1f3JN30 £061 4d AfU * AVUdHif0 co; 11 C = US flVU Mi SNUIlfA33S0G 30 330HIIN
03 I dX3
dliuieuXQ - /C6 jb u 3 Lem i ■ 9 919^1 Table 7 - Detonation Velocity - Dynamite
FXP RD
NUMBER OF DRSFRVAT J ONS TN DAT A OFT - 0 1VK 00 SATURDAY * HAY 7 r 1707 77 GENERAL LINEAR MGDFI S PROCEDURE DEPENDENT VARIABLE! VEL SOURCE DF SUM OF SOI. 1 ARES MEAN S nil ARE F VAI.MF MODEL 1 5021678.02909093 5021A78.02909093 4*07 ERROR A 7372401.97090907 1223733.66181018 RR F CORRECTED TOTAL 7 12394000.00000000 0.0077 K-SDUARE C.V. ROOT MSE VEL MEAN 0 * 405167 A♦1002 1108.48259428 ■ 1 HI 47.50000000 SOURCE DF TYPE I SS F VALUE PR > F
EXP 0 0.00000000 * 4 DR 1 5021A78.02709093 4.09 0.0397 UT 0 0.00000000 * *
DR#EXP 0 0.00000000 * 4
IJT*EXP 0 0.00000000 * * DR*UT 0 0.00000000 4 • DR*UT*EXP 0 0.00000000 » 4 SOURCE DF TYPE III SS F VALUE PR > F
EXP 0 0.00000000 4 4
DR 0 0.00000000 4 * UT 0 0.00000000 • 4
DR*EXF 0 0.00000000 4 •
UT*EXP 0 0.00000000 4 4
DR#UT 0 0.00000000 4 4
DR*WT#EXP 0 0.00000000 4 4 Table 8 - Scaled Peak Shock - Water Gel
r .r TUX
NUMBER DF" OBSERVATIONS TN PAT A SET ~ 8 14 :on SATURDAY ? HAY 2, 1987 12 FifNrRAi i TiTAR norm s ppnrrruiRr DEPENDENTvariable : ps SOURCE nr SUM OF SnilARFB MEAN BGUARF MODEL i 20923? » 69248073 P0923?.6924S073 ERROR A 7A7J 2,08771.978 4I /n"?nr , >’K> ♦ «■* *J 7r> JO/,' r** -* o\ «t CORRECTEDTOTAL 7 285951.78020000 Ft-SGUARE C.V. ROOT MSE PS MFAN 0.731731 .1. A . 7007 113.07231294 7 AH.74500000 SOURCE BE TYPE T SB F. VALUE PR > F
EXP 0 0.00000000 * » DR 1 209239.A?248073 1 A.37 0.0068
UT 0 0.00000000 4 * DR*EXP 0 0.00000000 4 4 UT#EXP 0 0.00000000 * * DR*UT 0 0.00000000 >, A
DR*WT*EXF 0 0,00000000 4 4 SOURCE DF TYPE TIT SB F VALUE PR > F
EXP 0 0.00000000 * 4
DR 0 0.00000000 4 4
WT 0 0.00000000 4 4
DR*EXP 0 0.00000000 4 *
HT#EXP 0 0.00000000 * 4
DR*UT 0 0.00000000 « 4
DR*WT*EXP 0 0.00000000 * * Table 9 - Shock Energy - Water Gel
EXP TUX
NUMBER OF OPSFRVATiriNS TN BATA SET = 0 1 -4 : on SATURDAY . MAY 2 r GENERAL LINEAR MODELS PROCEDURE DEPENDENT VARIABLEt 3E SOURCE DE SUM OF SQUARES MEAN SQUARE E VAI HE MODEL .1 ei.SS0.S71.40820 SI200. 5714SS20 101.14 ERROR 6 4821.74B46467 S03.62474411 PR > F "7 CORRECTED TOTAL / 06102.31995208 0 . 0001. K-SQUARE C.V. ROOT MSE SE MEAN 0.944000 15.4346 20.34027506 1.83. 66712500 SOURCE DE TYPE I SS r- VALUE PR > F EXP 0 0.00000000 4 • * DR 1 01200.57140020 101,14 0.0001 UT 0 0.00000000 *» DR#EXP 0 0.00000000 * t UT*EXP 0 0,00000000 « t DR*UT 0 0.00000000 « 4 DR*UT#EXP 0 0.00000000 * 4 SOURCE DE TYPE III SS E VALUE PR > F EXP 0 0.00000000 #* DR 0 0.00000000 • ♦ WT 0 0.00000000 * 4 DR*EXP 0 0.00000000 4 4 WTfcEXP 0 0.00000000 ♦ 4 DRfWT 0 0.00000000 • 4 DR#UT*EXP 0 0.00000000 * 4 Table 10 - Bubble Energy - Water Gel
FT XT’ U'y
NUMBER OF OBSERVATTONS TN DATA SET 0 14 105 SATURDAY. HAY ■j m ? 1 n GENERALLINEAR MODELS PROCFDURF DEPENDENTvariable : DE SOURCE DF SIJH OF SQUARES MEAN soil ARE r UAI ME MODEL 1 1070 * 530A32O3 13?0.53S/>5303 0./.4 ERROR 6 1 704.1. ,09095397 2973.X49035AA PR r CORRECTEDTOTAL 7 19732.43750/(00 0.455/. R-5BUARE ' C.V. ROOT MSE DE MEAN 0.09500? 1.3,4420 54.531 1.02.14 405.A5250000 SOURCE DF TYPE T SS F VAI 1 IF PR > F EXP 0 0.00000000 * ft DR 1 .1.090. 530/>3203 0./.4 0.455A WT 0 0.00000000 « * DR#EXP 0 0.00000000 t ft WT#EXP 0 0.00000000 ft ft DR#UIT 0 0.00000000 ft ft DR*WT*EXP 0 0.00000000 ft ft SOURCE DF TYPE TIT SS F VALUE PR > F EXP 0 0.00000000 ft ft DR 0 0.00000000 • ft WT 0 0.00000000 ft ft DR*EXF 0 0.00000000 ft ft WT*EXP 0 0.00000000 ft ft DR#WT 0 0.00000000 ft ft DR*WT*EXP 0 0.00000000 ft ft
u> Table 11 - Total Energy - Water Gel
EXP TUX
NUMBER OF DBSFRVATinNS TN BATA SET = R 1 4 i or; SATURDAY. MAY 1 "07 nn GENERAL LINEAR MODELS PROCEDURE DEPENDENTvariable : TE SOURCE BE SUM OF SQUARES HEAR SQUARE ' VAI ITF MOITEL 1 1 19029.55494343 119077,55494343 56. 05 ERROR 6 17740.93961P53 3.173.40993643 PR > F CORRECTED. TOTAL 7 131770.49456200 0.0003 R-SQUARE C.V. ROOT MSE TF MEAN 0.903310 7.4471 4A.08134044 6 lEl* 70550000 SOURCE DF TYPE I SS F- VALUE PR F EXP 0 0.00000000 * 1 DR 1 119029.55494343 56.05 0.0003 WT 0 0 . 0 0 0 0 0 0 0 0 BR*EXP 0 0,00000000 * » WT*EXP 0 0 . 0 0 0 0 0 0 0 0 » 4 PR*WT 0 0,00000000 ♦ * DR*WT*EXP 0 0 . 0 0 0 0 0 0 0 0 • ♦ SOURCE BE TYPE ITT SS F VALUE PR > E EXP 0 0 . 0 0 0 0 0 0 0 0 4 ♦
PR 0 0 . 0 0 0 0 0 0 0 0 • * WT 0 0 . 0 0 0 0 0 0 0 0 4 ♦ DR#EXP 0 0 . 0 0 0 0 0 0 0 0 • * WT*EXP 0 0 . 0 0 0 0 0 0 0 0 f 4 PRfcWT 0 0 . 0 0 0 0 0 0 0 0 « ♦ DR#WT*EXP 0 0 . 0 0 0 0 0 0 0 0 « * o> -c» Table 12 - Detonation Velocity - Water Gel
EXP 1 TUX
mumper nr odservations tn data set = o 14105 SATURDAYr HAY 2r GENERAL LINEAR MODELS PROCEDURE DEPENDENT VARIABLE' VEL SOURCE DF SUM OF SQUARES MEAN SQUARE E VALUE MODEL 1 4843645.44727274 4043645.44727274 1 .74 ERROR A 16730390.55272730 2788399.42545454 PR > E CORRECTED TOTAL 7 21574036.00000000 0.2356 R-SQUARE C.V. ROOT MSE VEL MEAN 0.224513 12.0137 1669.B49Q2123 13999.50000000 SOURCE DF TYPE I SS F VALUE PR > F EXP 0 0 . 0 0 0 0 0 0 0 0 * * DR. 1 4043645.44727274 1.74 0.2356 WT . 0 0 . 0 0 0 0 0 0 0 0 4 4 DR*EXP 0 0 . 0 0 0 0 0 0 0 0 4 4 WTfcEXP 0 0 . 0 0 0 0 0 0 0 0 « 4 DR*WT 0 0 . 0 0 0 0 0 0 0 0 4 4 DR*WT#EXP 0 0 . 0 0 0 0 0 0 0 0 4 4 SOURCE DF TYPE III SS F VALUE PR > F EXP 0 0 . 0 0 0 0 0 0 0 0 4 4 DR 0 0 . 0 0 0 0 0 0 0 0 • 4 WT 0 0 . 0 0 0 0 0 0 0 0 4 4 DR*EXP 0 0 . 0 0 0 0 0 0 0 0 4 4 WT#EXP 0 0 . 0 0 0 0 0 0 0 0 * t PR*WT 0 0 . 0 0 0 0 0 0 0 0 * ♦
DR*WT*EXP 0 0 . 0 0 0 0 0 0 0 0 4 4 CT* CJ1 66 Tables 6 and 11 give the responses of the fixed variables to total energy. Here, TE energy is significantly affected. Tables 7 and
12 indicated again that the most significant relationship exists between decoupling ratio and detonation velocity. I t shows in
Table 7 that the dynamite is l i t t l e affected by decoupling ratio, whereas the water gel is more significantly affected as shown in
Table 12.
4.2 RELATIONSHIPS BETWEEN SHOCK ENERGY, BUBBLE ENERGY AND DECOUPLING m n s ------
From the collected data, several comparisons were made between shock energy, gas energy, total energy and decoupling ratio.
4.2.1 Bubble Energy: Figures 21, 22 show bubble energy versus decoupling ratio . The bubble energy did not reach its maximum value until a decoupling ratio of approximately two, rather than at a value of one as would have been expected under the established theory.
This phenomenon occured for both the dynamite and the water gel.
Figure 23 plots both explosives against decoupling ratio for compar ison. The magnitudes of change in the bubble energy versus change in decoupling ratio were very similar for both explosives.
The study shows that as decoupling increases from 1 to 3.2, the bubble energy does not reach its maximum until a decoupling ratio of about two.
Persson (72) found that the most affected occurances were when the borehole diameter was twice that of the charge diameter. Britton (21), Paithanker (69) and Warden (86) published data with similar Bubble Energy (ca l/g ) 0 0 2 - 0 0 4 BOO-I - 0 0 6 0.0 - 1.0 iue Bbl Eeg versus Energy Bubble . 1 2 Figure eopig Ratio Decoupling eopig Ratio Decoupling 2.0 3.0 4.0 67 Bubble Energy (co l/g ) BOO—i 0 0 2 —I 400 - 0 0 6 0 j 1 I I I I I 1 I 1 | I I I I I I 1 I I | I II I I I I I I | ( I I I I I I I I | 0 10 . 30 4.0 3.0 2.0 1.0 .0 0 - iue Bbl Eeg versus Energy Bubble . 2 2 Figure eopig Ratio Decoupling eopn r tio ra DecoupKng Dynamite 68 Bubble Energy (ca l/g ) 200 400 -1 0 0 8 - 0 0 6 - 1.0 iue Bbl Eeg vereue Energy Bubble . 3 2 Figure eopig Ratio Decoupling eopig Ratio Decoupling 2.0 3.0 Water Water Gal 4.0 69 70
resu lts. These studies seem to valid ate the responses here. That 1s, bubble energy in a confined borehole is the primary source of useful
work.
These studies all used different explosives and broke a variety
of materials; therefore, the results were not biased by some inherent
phemenon.
4.2.2 Shock Energy: Figures 24, 25, 26 depict shock energy versus
decoupling ratio for both explosives. The change in magnitude with
decoupling ratio is again similar. The fact that shock energy
decreases with decoupling is significant since bubble energy increases
from a decoupling ratio of one to two. Therefore, bubble energy makes
up the larger percentage of total energy at decoupling ratios greater
than one.
Experiments conducted by Atchison (10) and Duvall (39) in several
rock types and different explosives found that the amplitude of the
strain pulse diminished while decoupling ratio increases. This does
not contradict the findings in this study, because the type of energy
they measured was shock energy. This study showed the same decline in
shock energy as these two researchers witnessed. It should also be
noted that they believed in the theory that shock energy is the pri mary force responsible for breaking rock and that gas energy rose
rap idly and s w iftly diminished through the stemming, while the stress wave caused scabbing of the burden. This study and previous studies at OSU have all shown that the gas energy does not diminish, but if
properly confined continues to work after the shock energy begins its Shock Energy (c o l/g ) 200 - 0 0 4 i - 0 0 8 600 0.0 - 1.0 iue Sok nry versus Energy Shock . 4 2 Figure eopig Ratio Decoupling eopig atio R Decoupling 2.0 3.0 Wotar l o C 71 Shock Energy (c o l/g ) 200 - 0 0 4 0 0 6 - 1.0 iue Sok nry vereus Energy Shock . 5 2 Figure eopig Ratio Decoupling eopig Ratio Decoupling 2.0 .0 3 .0 4 72 Shock Energy (c a l/g ) 200 8 - 0 0 4 - 0 0 6 OO 1 - 1.0 iue Sok nry versus Energy Shock . 6 2 Figure eopig Ratio Decoupling x eopig Ratio Decoupling 2.0 .0 3 Oet .0 4 73 74 decline, especially in decoupled boreholes.
4.2.3 Summary: If an explosive charge is properly confined, the gas energy will be the most effective force for doing useful work. It was also discovered that at decoupling ratios of about two, the gas energy is at its highest. It was also noted that the maximum break age occured at th is range of decoupling.
The role of shock energy in confined boreholes becomes less and less significant as decoupling ratio increases. At decoupling ratios of one, it causes excessive crushing about the boreholes, and in s it uations where the remaining wall is to be kept in tact, cracking occurs.
This study, along with past work, substantiates the role of gas energy and contradicts the established theory that shock energy is the primary mechanism for doing useful work in confined boreholes.
4.3 DETERMINE CAUSE OF ENERGY LOSS
Energy loss could res u lt from various sources. Channel or plasma e ffe c t and lack of confinement are the two phenomena most likely to affect energy loss. Their effect can be seen in the detonation velocity of a particular type explosive.
4.3.1 Detonation Velocity: Figures 27, 28, 29 plot detonation velocity versus decoupling ratio. The detonation velocity for the dynamite was rated by the manufacturer at 16,000 feet per second. In all the shots fired using this dynamite, the measured detonation v elo city ranged from a low of 16,326 to a high of 20,832 fe e t per Detonation Velocity ( X 1000 fpe) 0 2 - D I - 1.0 iue Dtnto Vlct versus Velocity Detonation . 7 2 Figure eopig Ratio Decoupling eopig Ratio Decoupling 2.0 .0 3 oo Oet Wotor .0 4 75 Detonation Velocity ( X 1000 fps) 0 2 10 - - 1.0 iue Dtnto Vlct versus Velocity Detonation . 8 2 Figure eopig Ratio Decoupling eopig Ratio Decoupling 2.0 .0 3 .0 4 76 Detonation Velocity (X 1000 fp *) 0 2 10 0.0 - - 1.0 iue Dtnto Vlct versus Velocity Detonation . 9 2 Figure eopig Ratio Decoupling eopig Ratio Decoupling 2.0 .0 3 .0 4 77 78 second. Also, the detonation velo c ity of the water gel ranged from a
low of 12,356 to a high of 15,744 feet per second, and the manufact
urer rated this explosive at 16,728 feet per second. It should be
noted that the widest range of detonation velocity for this water gel
was found 1n the fu lly coupled shots.
Figure 29 also shows that as the decoupling ratio Increased from
1 to 3.2, the detonation velocity dipped at a decoupling ratio of 2.4
and rose again at 3.2. Also, Figure 30 relates the shock loss factor
to decoupling ratio. It shows that the water gel is affected more
than the dynamite. The interesting thing 1s that both explosives
partially recover between decoupling ratios of two and three. This
indicated that plasma effects were minimal.
Although the detonation velocity did flucuate with decoupling,
in the case of dynamite, i t did not seem to be a res u lt of channel effects. The dynamite maintained faster detonation rates than that
rated by the manufacturer. The water gel, however, exhibited rates
less than forecasted by the manufacturer, but they were all within
reasonable limits and consistant at each decoupling ratio. The most errattc was at a decoupling ratio of one. The velocity values for dynamite remained especially close at each decoupling ra tio .
It was concluded that the major cause of fluctuation in measured detonation velocity resulted from lack of confinement and to incon sistencies that arise in normal manufacturing processes, and In the case of the water gel, some small amount of retardation could have resulted from channel or plasma e ffe c ts . Shock Loss Factor 2.0 .5 2 1.0 1.5 1.0 iue Sok os atr versus Factor Loss Shock . 0 3 Figure eopig Ratio Decoupling eopig Ratio Decoupling 2.0 .0 3 .0 4 79 80 Udy (85) studied plasma effects 1n decoupled pipe charges, and he found retardation in some explosives, total dead pressing In others and some explosive types were not affected such as PETN and dynamites. He also found that impregnating the charge wrapper with wax stopped plasma generation.
This concurs with the findings 1n th is study, where the detona tion velocity remained about the manufactured rated rate for dynamite.
It may also explain in part why, for the water gel, the detonation velocity was a little slower than the manufacturer predicted rate, for Udy found that water gels were suceptible to plasma effects. Even so, the significance level of the effect of decoupling ratio versus the detonation velocity 1n the statistical model showed a profound effect on the water gel while signifying little effect toward the dynamite. In any event, the work of Udy, this study, and the statis tical output reflect that the lack of confinement does play a major role in the reduction of detonation velocity. If there was a slight effect due to plasma, it was negligible, especially in the case of dynamite whose detonation velocity remained higher than expected.
The water gel, also, fell within reasonable limits and was rather constant at each decoupling ratio. Both explosives seemed to behave as expected; that is, the loss of energy resulted from lack of con finement, and to some lesser degree channel effects.
4 .3 .2 Summary: Energy loss due to plasma effects or lack of confine ment were discussed. I t seems that the energy losses were a d ire c t result of confinement since both explosives were at their lowest at a decoupling ratio of two, and they were higher at decoupling ratios of three. 81 However, due to the greater loss suffered by the water gel and
the work of Udy, plasma could have had some small a ffe c t on this
explosive. The dynamite, however, showed stable results with slight
losses even though it followed the general trend of the water gel.
4.4 MAGNITUDE OF ENERGY LOSS DUE TO DECOUPLING
The total energy for the water gel ranged from 776.630 cal/g at
a decoupling ratio of 1 to 419.433 cal/g at a decoupling ratio of 3.2.
The statistical model determined the relationship between
decoupling ratio and total energy as significant. The source of this
significance was shock energy, because bubble energy was not pre
sented as a significant response. Figure 30 shows the shock loss
factor versus the decoupling ratio. The model showed strong signifi
cant responses to shock and total energies. This significance can be
seen in the following two paragraphs.
4.4.1 Total Energy: Figures 31, 32, 33 show total energy versus
decoupling ratio. Decoupling ratios of 1 to 1.6 depict an increase
in dynamite whereas the water gel is fairly constant. Both decline at about the same rate after that point.
4.4.2 Percent of Total Energy: Assuming that the maximum value of
bubble energy fo r any decoupling ra tio was equal to 100 percent of
the total available bubble energy, and that the same holds for shock energy, then a graph could be plotted showing the shock and bubble
energies as a percentage of total energy. Figures 34 through 39 are such plots. Total - 0 0 g? 4 0 0 2 ] - 0 0 8 - 0 0 6 0.0 - 1.0 iue Ttl nry versus Energy Total . 1 3 Figure eopig Ratio Decoupling eopig Ratio Decoupling 2.0 04.0 4 .0 3 M 82 Totol Energy (c o l/g ) -1 0 0 8 0 0 2 - 0 0 4 6 0 0 — 0 0 6 .0 0 -
II I I I II |II I II II I I ri’l 1.0 iue Ttl nry versus Energy Total . 2 3 Figure
eopig Ratio Decoupling eopig Ratio Decoupling 2.0 I'TTTT
0 4.0 4 .0 3 I I | I I I l Dynamite 83 Total Energy (cal/g) 0 0 2 0 0 4 8 0 0 —| 0 0 8 - 0 0 6 0.0 - 1.0 iue Ttl nry versus Energy Total . 3 3 Figure eopig Ratio Decoupling eopig Ratio Decoupling 2.0 04.0 4 .0 3 84 85 Figures 34, 35, 36 represent a plot for water gel as percent of total energy versus decoupling ratio for both shock and bubble energy.
Figures 37, 38, 39 depict dynamite as percent of total energy versus decoupling ra tio fo r both shock and bubble energies. These graphs show at a decoupling ratio of one, the shock energy dominates, but it diminishes rapidly as the decoupling ratio Increases. The gas energy, however, continues to work and does not reach its maximum until a decoupling ratio of about 2.6 is attained. For example, if the decoupling ratio is one, the shock energy was at 100%, while the bubble energy was only 68%. At a decoupling ratio of two, shock dropped to 75%, while bubble increased to 98%, As the decoupling ratio goes to three, shock energy continues to drop to 26%, while the bubble energy remains high at 85%. The data are found in Table 13,
Atchison and Duvall together and in different studies found that strain amplitude diminished with increases in decoupling ratio. This study also found that the increased decoupling produced decreases in the shock energy levels. However, Duvall stated th a t gas pressure increased very rapidly and diminished rapidly, performing no useful function, while this study showed that gas energy 1n decoupled holes perform the useful work. This contradicts the established theory.
4 .4 .3 Summary: The source which produces to ta l energy loss is seen in the relationship between shock energy and bubble energy. That is , only when one looks at the percent of total energy that each of the basic energies contribute, is the picture made clear. In confined shots, shock energy as a percent of total energy diminishes while Psrcsnt of Total Energy - 0 4 - D B 0.0 iue Pret Ttl nry versus Energy Total f o Percent . 4 3 Figure 1.0 eopig ai f Wae Gel ater W r fo Ratio Decoupling eopig Ratio Decoupling 2.0 .0 4 86 Percent of Total Energy - 0 4 - 0 B iue Pret Ttl nry versus Energy Total f o Percent . 5 3 Figure 1.0 eopig ai f Wae Gel ater W r fo Ratio Decoupling eopig Ratio Decoupling 2.0 .0 3 Bubble .0 4 87 Percent of Total Energy - 0 4 - 0 8 0.0 iue Pret Ttl nry versus Energy Total f o Percent . 5 3 Figure 1.0 eopig ai f Wae Gel ater W r fo Ratio Decoupling eopig Rotio Decoupling 2.0 .0 3 .0 4 88 Percent of Total Energy - 0 4 0 6 0.0 iue Pret Ttl nry versus Energy Total f o Percent . 7 3 Figure 1.0 eopig ai f Dnmite Dynam r fo Ratio Decoupling eopig Rotio Decoupling 2.0 .0 3 .0 4 89 Percent of Total Energy - 0 4 - 0 8 iue Pret Ttl nry versus Energy Total f o Percent . 8 5 Figure 1.0 eopig ai f Dynamite r fo Ratio Decoupling eopig Ratio Decoupling 2.0 .0 4 90 Percent of Total Energy - 0 4 - 0 8 0.0 iue Pret Ttl nry versus Energy Total f o Percent . 9 3 Figure 1.0 eopig ai f Dnmite Dynam r fo Ratio Decoupling eopig Ratio Decoupling 2.0 04.0 4 .0 3 91 Table 13 - Percent Total Energy
WATER GEL DYNflMITE
D/R % ll (Shock) % ll (Bubble) %TE (Shock) %TE (Bubble)
1 100 85 100 68
1.6 72 100 83 98
2.4 38 99 40 100
3.2 18 76 22 80
D/R = Decoupling Ratio
TE = Total Energy 93 gas energy as a percent of total energy Increases with increases in decoupling ratio up to about two.
4.5 ARE THE EFFECTS LIMITED TO ONE GENERAL PHENOMENON?
To consider this question, one must make a lis t of factors that could contribute to the energy loss in decoupled holes. Number one would be the type of explosive used. In th is case, a dynamite and a water gel were used, B ritto n 's laboratory te s t used PETN while
Paithanker used s till another explosive in his field tests. Atchison and Duvall used various explosives. All obtained similar results.
Therefore, there is no effect from a particular type explosive.
The second phenomenon could be the m aterial to, be broken. Here, too, a variety of materials were used and s till with similar results.
So material response is not a significant problem.
A third consideration might be charge weight, but by the statis tic a l model fo r th is study and fo r Bhushan's (14) study; as well as, the others lis te d above gave no notion of being a casual e ffe c t.
The only phenomenon th at was common to a ll the studies was the lack of confinement. When a charge is not properly confined, the gases cannot work; they are dissipated. But when they are confined in holes decoupled or coupled the explosive acts more efficiently.
The results of this study show that the only common phenomenon found to affect energy loss is loss of confinement; that is, the bigger the annul us around a charge the more energy is used up by the gases expanding into this void before beginning useful work. 94
In coupled shots the excess shock energy Is used up crushing
rock around the borehole producing excess fin es.
4.6 CONCLUSIONS
The purpose of this study was to demonstrate that the established
theories concerning decoupling were not completely valid. Also, an
attempt was made to establish the role of gas energy as the dominate
mechanism for doing useful work by an explosive in boreholes where
the explosive could be properly confined.
In decoupled boreholes, the total energy released is composed of
two types—shock energy and bubble energy. At a decoupling ratio of
one, shock energy is at its highest, and it diminishes rapidly with
each higher decoupling ratio. The gas energy, however, reaches its
peak a t a decoupling ra tio of about two a t which time i t begins to diminish as decoupling ratio Increases. It decreases at a slower
rate than does the shock energy. Therefore, it can be concluded that
bubble energy has the mechanism potential capable of doing the most efficient work 1n decoupled holes, and all boreholes not bulk loaded are by necessity decoupled.
It was also shown that neither explosive or rock type had any effect upon the explosive's ability to generate effective energy to do efficient work. For dynamite, water gel and PETN, plasma effects were minimal or not present a t a l l . Too, the e ffe c t seemed to be dominated by the bubble energy; th at is , the bubble size or the amount of generated gases correlates well with energy release and with 95 breakage. See Appendix I for details. Therefore, It can also be concluded that coupled shots suffer from non-1deal detonation which contradicts the established theory that Ideal conditions exist only
1n fully coupled boreholes. If the established way of looking at efficient detonation were true, then one would expect lower detona tion velocity rates as decoupling Increased. This was not the case.
Velocity only dropped s lig h tly from a decoupling ra tio of one to a decoupling ratio of two.
The effects of bubble energy at a decoupling ratio of one was less e ffe c tiv e . I t 's when the bubble energy dominates th at the explosive is most effective.
4.7 FUTURE RESEARCH
Through several research projects conducted a t The Ohio State
University, it has become apparent that gas energy or borehole pressure 1s an effective tool for breaking rock.
Other experiments Involving decoupling would be of interest to determine just what happens at a decoupling ratio of two; that is, to learn why it plays such a significant role in energy utilization.
Comparisons might be made using a wider range of decoupling ratios. Although they are not practical in present blasting practice, their presence could establish a more clear picture for comparison purposes.
It would be good to use a larger variety of charge sizes and length to burden ratios to determine their effect on energy efficiency. 96 Full scale shots measuring times from detonation to face break age, shock waves, detonation velocity, borehole pressure, seiving and weighing the broken m aterial would produce concrete relationships between D/R and breakage, D/R and borehole pressure, breakage and borehole pressure. I t would also allow fo r comparisons between shock energy and D/R and shock and breakage with relavent detonation v e lo c ities and detonation to breakage times. These comparisons could clear up some of the mystery surrounding the decoupling ratio of two phenomenon, as well as the non-ideal detonation that takes place at the decoupling ratio one. In summary, further studies which measure borehole pressure and evaluate its components, such as, Cy/Cp r a tio , calculation methods and loading could lead to more efficient and cheaper field use of explosives.
° Strain Amplitude, Nicholls (63)
100
- i i * e
©
1 2 3 4 Decoupling Ratio
Figure 40 • Percent R e la tive S tra in Amplitude and Percent Shock tn e rg y fo r Dynamite and Mater Del Versus Decoupling R atio APPENDIX A
PREPARATION OF MATERIALS
97 98
APPENDIX A
PREPARATION OF MATERIALS
Pipe I.D . Thickness Spacer O.D. (inches) (inches) (inches) D/R
1.250 0.125 none 1.0 2.000 0.125 1.9375 1.6 3.000 0.1875 2.9375 2.4 4.000 0.250 3.9375 3.2
A ll spacers were made from \ inch thick pine, and they had an inside diameter of 1.3125 inches.
2. Dowel rods were h inch in diameter and 22 inches long.
3. The charges were 24 inches long, i.e. three l*s X 8 inch long sticks.
4. Pipe caps were standard caps used with this type of pipe. A
5/16 inch hole was drilled in the end for wire passage. APPENDIX B
Derivation of Relationships
In An Ideal Detonation
99 100
APPENDIX B
DERIVATION OF IDEAL DETONATION RELATIONSHIPS
Taylor (61), Cook (17), Mathias (47) and others show the follow
ing relationships for ideal detonation.
If the detonation is ideal, the shock front is flat and has a
longitudinal wave motion, Its thickness is negligible, and it is
treated as a discontinuity in comparison to the changes that occur
behind i t .
With these assumptions, the mass flow per unit area of shock
fro n t into and away from the shock front becomes equal as dt -»■ 0 .
Mass flow into shock fro nt = Ap0 (V-UQ)dt (36)
Mass flow from shock front = Ap (V-U)dt (37) where A - u n it area of shock front
(V-U ) - the velocity of the mass flow from shock front
V - shock wave v elo city
UQ - initial particle velocity
U - streaming velocity of the detonation products
pQ - density of the undetonated explosive
p - density of detonation products
dt - an infinitesimal time interval 101 Since energy is conserved, the mass flow into is equal to the mass flow from the shock front over time dt.
Ap0 (V-uo)dt = Ap(V-U)dt (38)
Since dt ■+■ 0:
po(V“U0) = p(V“U) (39)
The momentum of the mass flow into the shock front over time dt is:
AP0 (V- Uo)Uodt (40)
And the momentum of mass flow from the shock fro nt is:
Ap(V-U)Udt (41)
Since po^”^o^ = (^- 6 ) becomes:
Apo(V"Uo)Udt (42)
Because the difference between the momentum of mass flow from the shock front and the mass flow into the shock front over time dt is equal to the difference in impulse, dl. *
dl = Fdt - F dt (43) o where F = the force exerted by the mass flow from the shock front
Fq = the force exerted by the mass flow into the shock front because F = PA (44) 102 where F * force
P * pressure
A » area
equation (B- 8 ) becomes)
dl - PAdt - P0Adt (45)
Combine equation (B-5), (B-7), and (B-10), then;
*>0(v- as the 1 imit dt -* 0 : P0 tV-U0 )(U-U0) - P.P0 (47) If U =0. equation (A-4) becomes p(V-U)=p0U (48) (B-13) can be transposed to: V * PU/(P-P0) (49) If UQ * 0, equation (B-12) becomes: P - po - PoVU (50) (B-15) can be transposed to : U - (P-P0 )/(*V > Substitute (B-16) Into (B-14) gives: v - p ( p - p 0)/C (p - p0 ) ( p 0v )) which reduces to : V = Ap/p0 )UP-P0 )/Cp-p0 )) and v2 - tP/P0 )((P-P0 >/tP-P0 )) Substitute (B-15) Into (B-19) gives: V2 - (pP0VU/tp0^P"Po^ which reduces to: APPENDIX C EXPLOSIVE DATA 104 105 APPENDIX C EXPLOSIVE DATA Austin Powder Company, Red D dynamite (perm issible) E. I. duPont de nemours and Co. (Inc.), TR-2 watergel (permissible) Manufacturers' Data Data Red D TR-2 Density 1.35 g/cc 1.25 g/cc Detonation Rate 16,000 fps 16,728 fps Detonation Pressure 81 kb Weight Strength 955 cal/g Bulk Strength 1289 cal/cc 1172 c al/cc Water Resistance Excellent Excellent Weight/lV'x 8 " Cartridge 2 1 1 grams 2 0 1 grams Stick Count/50 lbs. 103 113 Cap Sensitive # 8 cap # 8 cap APPENDIX D DETONATION VELOCITY TRACES 106 APPENDIX D DETONATION VELOCITY TRACES Figure 4 1 -1 .2 5 inch diameter pipe; TR-2 Figure 42- 1.25 inch diameter pipe; TR-2 Figure 43 -2.00 inch diameter pipe; TR-2 Figure 44-2.00 inch diameter pipe; TR-2 109 PR csu x :iee*v ;se.s j v z r e . e *V*-40.®»V ■ : AT* 201.BmS Figure 45 _3.00 inch diameter pipe; TR-2 Figure 46-3.00 inch diameter pipe; TR-2 Figure 47-4.00 inch diameter pipe; TR- Figure 48 -4.00 inch diameter pipe; TR Ill O S U 1 T P O S 1 C S U 1 2 V 12B * » S j V Z R - 2 . 2 AV— 7 . 8 V A T - 6 3 . 7 5 > , S Figure 49-1.25 inch diameter pipe; Red-D D S U 1 T P O S 1 C S U 3 : 2 V ; 2 0 v S V Z R - 2 .4 AV*- 6 . 8 V A T = 8 0 . 2 5 VS Figure 50-1.25 inch diameter pipe; Red-D Figure 51 -2.00 inch diameter pipe; Red-D Figure 52 -2.00 inch diameter pipe; Red-D Figure 53 -3.00 inch diameter pipe; Red-D Figure 54 -3.00 inch diameter pipe; Red-D 114 ^ jV *-,L'n *■> 1 * f : TPU. 1 r 1 2.M l 2V 20>)S A'Zk-2.7 iV = -e.€V . -iT =-,.102 Oi.£ Figure 55 -4.00 inch diameter pipe; Red-D Figure 56 -4.00 inch diameter pipe; Red-D APPENDIX E PIEZOELECTRIC GAGE SPECIFICATIONS 115 116 APPENDIX E PIEZOELECTRIC GAGE SPECIFICATIONS MODEL NO 138A05 Range { 5V Output) psi 5000 Useful Overrange psi 1 0 0 0 0 Maximum Pressure psi 50000 Resolution psi 0 . 1 Sensitivity mV/psi 1 Resonant Frequency MHz 1 . 0 Rise Time (In Water) uSec 1.5 Discharge Time Constant Sec 0 . 2 Low Frequency Hz 2.5 L in e a rity %?$ 2 P o larity Positive Output Impedance ohm 1 0 0 Output Bias (Nominal) v o lt 1 0 Overload Recovery uSec 1 0 Temperature Range °F 0 to 1 0 0 Shock (Mechanical) G's peak 2 0 0 0 0 Sealing Nylon Tied Case/Diaphragam M at'l Tygon & Nylon D elrin 117 Weight gm 21 Connector (micro) coaxial 10-32 Size (DIA x LG) in 0.37 x 7.6 118 .15 ELECTRICAL CONNECTOR COAXIAL 10-32 UNF-2A IN-LINE AMPLIFIER SIGNAL £ GROUND WIRES SENSING ELEMENT SILICONE OIL LEAD WIRE HOLE FOR WEIGHT ATTACHMENT .37 OIA Figure 57 - The Piezoelectric Gage (After Bhushan (14)). 119 AC VISIONS fCB SERIES 136A MODEL JCP TOURMALINE UNDERWATER PROBE PIS OPERATING GUIDE SNCET 1 W 2 1.0 TMTRDDtTTIpN The PCE S e rie s 1 )6 * is a v o lta g e mode the souree clement transforms this input tourmaline transducer specifically De i n t o s low impedance signal of equal am signee for operation unoervater or in plitude. The DC bias that exists on the liquids Compatible with tygon and nylon. signal lead is blocked from the output by (See Specification Sheet in the front eT a coupling capacitor in the PCS power this manual for range and sen sitivity). u n it s i. The Series DBA features a b u ilt-in 1CP 2.0 INSTALLATION am plifier which converts the high impedance voltage from the crystals into a low im- Connect a 10-32 coaxial cable to the peeencc voltage or less than 100 ohms. transducer connector and-seal against m oisture. Observe output on scope, meter Power to operate the IC am plifier and the or recorder. Mote that system responds output signal are conducted over a single only to changing inputs: if static force conductor coaxial cable w ith a shield is applied, the signal decays back to serving as signal return. Special low z e r o . ncisc cables are not required. 5uspend the Scries 136A in the liouid The Series DBA is used by the m ilitary where measurement is tc take place. A for unoerwater explosive testing, for small hole is provided in the conical com m ercial use in g a s o lin e ta n k s and_ section of the prooe so that a light transformer shock wave applications.' The weight can be attached to suspend the transducer is idea) for monitoring dy sensor at deeper levels. The line should namic pressures because it exhibits non- be of lig h t m aterial (monofilament, 15 lb re sonant response. test) to enable it to break easily so nrzKnmuc that the transducer does not pul) apart E.51X: in the turbulence caused by the collapse or the gas bubble resulting from the shock wave. 3 .0 QPERATTQN It is necessary only to supply the trans ducer w ith a 2 to 20mA constant current at *1B to -2AVD0 through a current re gulating diode or equivalent circuit. See Guide C-000) for powering and signal utilizatio n information pertaining to all ICR instrum entation. L _ Most PCS power units have an adjustable current feature allowing ■ choice or in put currents from 2 to 20mA. In general, for best resolution chccse the lower current ranges, and for driving long nc. 1 SCHEMATIC, I CP TRANSDUCER cables (to several thousand feet) use the higner current, up to 20mA maximum. Line The charge generated by deflection or the impedance eialching may be necessary te piezoelectric element when subjected to produce fla t freouency response over long shock wave, creates a voltage on the in (hundreds or thousancs of feet) cables. put capacitance at the gate of the ampli f i e r . The a n c l i f i e r in c o n ju n c tio n w ith 120 "I vis>0<5 PCS SERIES 13SA MODEL ic p t o u r h a u n j : undcrw atcr probe »«■m OPERATING GUIDE fH itT or 2 3.0 QPERATIQ*j (eont'd) Switch power on end observe reading o f bias 2. If AC coupled at the power unit, the monitoring voltmeter on front panel of powercoupling time constant. u n i t . Consult Sections £.0 through £.2 in Gen If indicator it in green section of indi eral Cuide C-0001 for detailed explana cator panel, the 1C am plifier is*producing tion of low frequency characteristics or proper bias (-11VDC), cable connections are ICP instruments. normal and the system is ready to operate. T.O HA TNTFMAhtf AMD REPAIR If the needle aevcs to the red area of the fault monitor meter, output la zero and a It is well to observe the following pre short is indicated. Short could be located cautions in using the transflucer: in am plifier, cable connectors, or power u n i t . 1. Do not exceed specified maximum ra n g e . If pointer moves into the yellow area of the fault aionitor aieter, an open circu it 2. Do net subject transducer to tem is indicated with fu ll power supply voltage. peratures exceeding 10C f. An open circuit could be the result of a TauJty am plifier, an open cable of open 3. Do not apply voltage to transducer connectors. without current-lim iting diooes or croer current protection. Allow the transducer to stabilise for about one minute. A signal C rift «*ay occur when A. Do not apply mere than 20mA of cur cable is connected to the readout instrument. rent to the transoucer. This d rift oeeurs during charging of the I f th e S e rie s 13BA p ro b e i s damaged by couoling capacitor in the power unit. The the gas bubble whieh coll asses after the signal w ill staciliie in several minutes. shock wave, please return the senscr to the factory fcr repair with a note de a .D CALIBRATION' scribing the malfunction cr problem. The Series 136A is calibrated dynamically using a crop weight tester. For best ac curacy use the calibration certifica te supplied, rectory recalibration is avail able for a nominal charge. S.D PCLAEITv This transducer series produces a positive- going output voltage for increasing pres sure input. £. 0 LOk' fEEOLJth-fY RESPONSE The low freouenry response of an ICP system is determined by: 1. The discharge time constant of the transducer. APPENDIX F UNDERWATER MEASUREMENT TECHNIQUES 121 122 APPENDIX F UNDERWATER MEASUREMENT TECHNIQUES Measurable underwater shock wave parameters are pressure and profile of pressure decay. Calculation of impulse and energy flux density, E^, require squaring and integration of the pressure pulse. Pressure decay, impulse and energy flux density for a shock wave are shown and defined 1n Figure 58. The time period, T, of the first oscillation of the gas bubble shown in Figure 58 is the most commonly measured gas energy parameter. Bubble energy of the explosive 1s proportional to the cube of T and inversely proportional to the 5/6 power of the sum of the atmospheric and hydrostatic pressures. The most commonly used instrument used to measure pressure in underwater explosions is the piezoelectric transducer. For this app lication, quartz or tourmaline crystals are good materials. Quartz has d irectio n al effects whereas tourmaline responds purely to hydro static pressure; therefore, It's the preferred material. Gage output is amplified and recorded on an oscilloscope. Gage manufacturers provide calibration data to enable conversion of voltage levels to pressure. Shock wave impulse levels are derived by measuring the area under the pressure-time curve, while shock energy 1 s determined from the area under the pressure squared versus time curve. Figure 59 shows a typical underwater test set-up and oscilloscope recordings. 123 OVERPRESSURE M I TIMC ni ka« oviMotiiim c m p e a k overpressure a o o v c a m o ie n t p r es s u r e (a s s u m e d TO U O f THE fO R M P ( tl- f- ,*'*/* l u t t im c c o n s t a n t ipj THE TIMC RE QUIRE 0 fO R THE PRESSURE TO P A L I TO A VALUE ©PP.* (Jl IMPULSE (II f * P(iM i CTHE INTEORATION TIMC 1 IS USUALLY T. I TO IE HI M l ENERGY PLUX DENSITY (El - 1 - (1-2.423 ■ IC^P - 1 .031 ■ lO ^P * | / 1 F^ltW i I.C. " • WHERE THE TWO NEGATIVE TERMS REPRESENT THE CORRECTION POR APTERPLOW. #.C . IS THE ACOUSTIC IMPCOANCC OF THE MEDIUM. (THE INTEGRATION TIME i IS USUALLY TAKEN TO RE SPI. Figure 58 - Underwater Shockwave Parameters (After Roth (76)). Figure 59 - Typical Underwater Test Setup and Results {A fter Roth (76)) 125 With cylindrical charges, the gage should be aligned perpendicular to the bisector of charge length. Using a 50 pound, 25 foot long TNT charge, off-the-s 1 de and off-the-end measurement differences are shown in Figures 60 and 61. The principle of similarity 1s the basis for shock wave scaling laws. Cole (27) explains this p rin cip le as: "Suppose that measurements of pressure have been made a t a d is tance r from a charge of specified dimensions a t a time t a fte r i t is initiated and that a new experiment is arranged in which all the linear dimensions of the charge are changed by a factor X. The prin ciple of similarity asserts that the pressure and other properties of a shock wave w ill be unchanged i f the scales of length and time by which i t 1s measured are changed by the same facto r X as the dimen sions of the charge. For example, the pressure and duration of the shock wave measured ten feet from a cubical charge one foot on an edge will be the same as the pressure and duration measured twenty feet from a charge two fe et on an edge 1 n units of time twice as large. The duration in absolute units is therefore doubled at the doubled distance for the charge of twice the linear dimensions (eight times larger weight)". Experimental verification of the principle is provided by Cole (2 7 ), Condon (2 9 ), and Roth (7 6 ). The p rin cip le permits measurements to be made at a fixed distance with a set of charge weights and results for any other charge weight can be calculated. Alternatively, measurements can be made with one charge weight at a set of distances and then predicted for any other distance. Once the mathematical \ INC CMMCC ^ y ^ v\yA ss v:y Figure 60 “ Shock Front front a Line Charge (After Roth (76)) PEAK PRESSURE ( tf l- B /lN * ) 2 0 .4 0 0.6 0.8 0.1 (.0 20 0 40 60 iue 1 Efc o Gg Lcto in Location Gage of Effect - 61 Figure ITNE O CHARGE TO OISTANCE F SlOE OFF ER END NEAR FAR newtr et { tr oh 76)). 6 (7 Roth fter {A Tests Underwater 20 END 4 (FT) 2 127 128 form of the dlstance-charge weight-time function Is determined, reasonably correct predictions can be made for pressures. I f chemical reactions behind the detonation front are Important, or if viscosity and/or gravity effects interfere with consistance, the principle of sim ilarity is not valid. In particular, the principle does not apply to motion of a gas sphere affected significantly by gravity. The following methods and equations follow the work of Cole (27). Cole stated that peak shock pressure, (Pn), 1s an important shock wave parameter where decay of peak shock pressure is exponential during the fir s t few miscroseconds. Therefore, pressure, P, as a function of time, t, after arrival of the shock front 1s given by: P(t) = Pne " t / 0 (57) where 6 is the time constant of exponential decay. The equation describes the so-called acoustical assumption of exponential decay for peak shock pressure. From the principle of similarity, at a given distance, R, the pressure must scale as linear. Dimensions of a charge are proportional to the cube root of the volume and thus 1/3 weight, W, while the pressure is proportional to W , Therefore, 1/3 scaled peak pressure Pn/W ' is a characteristic of the explosive for fixed test conditions. Time, also, scales a hence, e/W *^ is another characteristic constant. The impulse per unit area of the shock wave front up to a time, t, after its arrival is defined by: Kt) - /J P(t) dt (58) 129 Actually, the above equation should be the integral of {P(t ) - PQ) where PQ is the hydrostatic pressure. However, since PQ is negligible compared to shock energy and the distances of interest, PQ is eliminated. The duration of integration is usually taken to be 1/3 56, but since time and pressure are both proportional to W for 2/3 some fixed distance, the scaled impulse I(t)/W is another charact eristic constant of an explosive under fixed conditions. From fluid dynamics, the rate of energy transport across a unit area in a fluid of density p at a particle velocity y is given by: pU = A(E +.0.5y 2 + P/p) ( 5 9 ) 2 where (E + 0.5y ) is the increase in kinetic and potential energies for a unit mass of fluid, and P is the pressure. The energy flux density to time, t, after arrival of the shock wave is then given by: Ef = pyA{E + 0.5y 2 + P/p}dt (60) Because the amplitudes are small compared to P/p, the internal and kinetic energies may be neglected. Hence, for a spherical acoustic wave, the particle velocity at a given distance, R, and time, t ', is given by: u Ef ■ f V ' J ( « . ) * « + pJir'S (P-P0 )(/J '(p -P0 )dt>dt' (62) The second term representing the effect of the excess particle velocity or afterflow left by an outgoing spherical wave may be neglected compared to the f ir s t term for distances at which measure ments are conmonly made. Also, since PQ is small compared to P; i t too may be neglected. Thus: Ef » — J - P2 (t)d t (63) T °oo 0 The total shock energy at a distance, R, can be calculated by multiplying by the surface area of a sphere of radius, R. Hence, the total shock energy is given by: E = 4irR2 — jU P2 (t)d t (64) 5 Po 0 0 1/3 When R is fixed, pressure andtime are proportional to W and therefore Es is proportional to W under the acoustical approximation. The scaled shock energy, Eg/W, (i.e .* the shock energy per unit weight of explosive) is another characteristic constant of the explosive for fixed test conditions. The most important bubble parameter is the period of firs t oscillation. Its relationship with pressure PQ (atmospheric plus hydrostatic) and bubble energy of the explosive, Y, can be derived theorectically if vertical motion is neglected. For radial flow, the equations of continuity and motion for water are (27): 131 + + <6 5 > v i £ + w ! £ + I f " 0 (66> where p is density of water, r Is radial distance from charge center in units of charge radius, u is water velocity, P is pressure, and t is time from the instant of detonation. Due to changes in bubble pressure, the changes in density of - 4 water are of the order of 10 pQ where pQ is the equilibrium density. Therefore, neglecting the derivatives of p: iE = -2£E (67) 3r r or u (r ,t) = ^ T (68 ) r where the constant of integration U j(t) is the velocity for r=l and a function of time. Thus, the radial velocity of water is inversely proportional to the square of the distance from the origin. With this result, the second equation becomes: = » (69) r Integrating from the surface of the gas sphere, for which r=a 2 (bubble radius), u, = da/dt = u,/a , P=Pa, to infinite distance where a X a 132 P=PQ and u=0 gives: T - $ i af> - F (al )2 - (p- - p-> = 0 (7 0 ) Integrating with respect to time leads to the result; = (71) where C' is a constant of integration. Except for a factor 4 tt, the integral over the radius of the gas bubble, a, represents the work done by the pressure Pa in expanding the sphere to its radius a (t), 2 as the element of volume is dV=4Tra da, and the integral must therefore equal the decrease in internal energy of the gas to E(a) from its in itia l value. Absorbing this in itia l value into a new constant of integration, Y, gives after rearrangement: | P0 a3 > (£ )2 ♦ f P..3 ♦ E(a) - V ‘72> This equation represents conservation of energy. The f ir s t term is kinetic energy of radial flow, the second term is work done against hydrostatic pressure, and E(a) is internal energy. Therefore, Y represents total energy of the gas bubble. At the instant when the gas bubble is at its maximum, the internal energy of the gases is very small and may be neglected. Also, at that instant da/dt=0. Designating a=am or the maximum bubble expansion: Thus, for a known maximum bubble radius, am, the bubble energy, Y, can be calculated. Neglecting the Internal energy and sub stituting for Y gives: t - f , (74) o o {(V3 _ jjH where aQ is the in itia l radius of the gas sphere at time t=0. The closed form of this integral is mathematically non-existent. Numerical integration from a=0 to a=am; that is, over half the period of oscillation is: T ■ § % (75> In terms of bubble energy, Y: , vl/3 T-1-14po 757S (76) 0 This expression is commonly known as the W illis formula. I t is dimensionally correct. Therefore, i f T depends on pQ, Y, and PQ then this equation is more general than the simplistic assumptions made in its derivation. Numerous reports (27, 29, 76) substantiate the formula. Written in another form: 134 where = 0.67 pQ I f the pressure on the water surface is one atmosphere, or 33 f t . of water, and a charge is exploded at depth, d, then PQ is equal to (d+33) f t . of water. At a test site where the depth of charge is fixed, the W illis formula gives: Y - KbT3 (78) where all the conversion factors and fixed test constants are included in Kg. According to Cole (27), the bubble energy Y can usually be expected to be proportional to the weight of the charge. Therefore, the scaled bubble energy, Y/W, ( i . e . , the bubble energy per unit charge weight) is a characteristic constant of the explosive. Formulae Used for Underwater Explosive Evaluation 1. Sadwin et. a l, (77), were among the fir s t to use underwater test methods for evaluation of commercial explosives. They used the following formulae for data analysis: K T^ Bubble Energy,Eg = -§ — (79) Scaled Peak Pressure,P = ( PS*w%) (80) s lbV J Impulse, I « P(t)dt (PSI-sec) (81) Scaled Impulse,I = (P^* (®2) s lb c/J 135 Energy Density E- - K / * P 2 (t)dt (^4^) (33) T s 0 in and 4ttR2E, lh .. Shock Energy E$ = — ^----- (— ^ - ) (84) 2. Hercules Inc. has been using underwater testing methods since the early 1960's. The formulae they use are: and K. A P2 dt Es = -*-g------(86) To evaluate the constants Kg and Ks, a known weight of Pentolite 3 is fired under the standard test conditions. The values of T and 2 / P dt are calculated from the measurements of T and profile of P(t), Values of Eg and Eg for Pentolite are known. Therefore, K$ and Kg are available to calculate the energies of other explosives. 3. DuPont, (37), uses the following formulae for underwater evaluation of explosives: {5.5(d+2.31P)2’5}T3 - EnB = W where Eg = bubble energy (cal/g) T = period (seconds) 136 d = charge depth (ft) P = atmospheric pressure (psi) Q = heat of explosion of primer (cal/g) b = wt. of primer (lb) W = net charge weight (lb) The impulse is calculated as follows: ft P(t)dt Jo W ( 88) where t is taken to be 1 percent of the bubble period. 4. Bjarnholt and Holmberg, (16), of the Swedish Detonic Research Foundation suggest the following formulae: (89) where Kj = 1.135 Pw^/P^ 5/6 p hn ■ the normal total hydrostatic pressure at the given charge depth p h = the total hydrostatic pressure at the charge depth when t^ was measured C = constant which depends on the test site and must be determined experimentally This formula was derived to incorporate the physical effect of boundaries of the test site used for evaluating bubble energy. Shock energy at the point of measurement is calculated as follows: 137 (90) Total expansion work Aq done by a unit weight of explosive should be calculated as follows: Ao = Kf fEB + «Es} (91) where is a correction factor for charge geometry and p is a correction factor for shock energy lost as heat, (16). Standard values of for various charge shapes are given in Figure 62. The shock loss factor is considered to be dependent upon the detonation pressure alone. Detonation pressure is calculated from the measured detonation velocity V^. Pd = 0.25 p v * (GPa) (92) where pfi is the density of explosive. The correction factor must be determined from the graph of pvs.P^ shown in Figure 63. This graph was empirically developed by equating the calorimetric measurement of A to (E.+uE } for a number of explosives, o b s 5. Dyno Industries A.S. of Norway uses the following formulae, (88): (93) Eb = i (2.5T3) (3.28+33.95)2*5 (94) 138 k,- 1.00 k( - 1.08-1.10 k f - 1.02-1.03 kf - 1.00 Charge in Cylinder shaped charge Charge In Sphere initiated (M in t can with UD ■ 6 Erlenmeyer glau flask at the center Figure 62 - Shape Factor for Various Charge Shapes (After Bjarnholt (16)). 2 . 0 - 1.5 • («p«riw*nial point* 1.0 _ i__ 20 30 Figure 63 - shock Loss Factor ve.Detonation Pressure (After Bjarnholt (16)). 139 .-9 ..2i Ao = Kf ^ I -542+6*555 * 10 PeV Es+EB} ^ Symbols have been defined e arlier. 6 . IDL Chemicals Ltd. uses a similar set of formulae, (70): (96) Es ■ ^ 'I p2dt <* ■ lnK> E0 = 2.471 x 10 * 9 (d+4.4605 x 10' 2p)2 - 5T3/W (97) where T = bubble period in milliseconds d = depth of charge in f t . P = atmospheric pressure in mm of mercury W = wt. of charge in grams, and Eg is in kcal/g. 7. Condon et. a l, (29), of the U.S. Bureau of Mines claim that: Relative Shock Energy,(RSE) = (E )sample/(E )TNT (98) where Es = P2dt (99) {T(P_)5/6}3sample Relative Bubble Energy (RBE) = ------(100) {T(Po)5/6}3TNT Absolute values of shock and bubble energy are not evaluated. 140 8 . The Encyclopedia of Explosives and Related Terms, (76), gives the following formulae: I = P(t)dt (101) Es ' '* lk {1' 2A2Z * 10' 4pm-1-031 x 10' 8 Pm}/J "*<*>*(102) where the two negative terms represent a correction for afterflow, and t = 59. RBE ■ K = TPo5/ 6/W1 /3 (104) TNT and PETN are used as standard references for underwater evaluation of commercial explosives. The principle of similarity permits the following form of the equation to f i t a ll of the shock wave parameters (P , 9, I and E ): ill ^ 1/3 Parameters = K ( ^ — )a (105) Values of K and a for TNT and PETN are given in Table 14 (76). The period of first bubble oscillation, T, fits the following equation: K W1 /3 T = V „ (106) (d+33) /6 141 Table 14 -Similitude Constants for Standard Explosives (After Roth (76)). viV> Range 0/W ,/J E/V P,T1 of a Validity* Explosive K a K or K a K 2.04 3.4-138 TNT 52.4 1.13 0.064 —03 3 5.75 0 39 84.4 3.4-136 Pentolite 565 1.14 0.084 —03 3 5.73 051 92J0 2.04 103-136 H-6 593 1.19 OjOSS —03 6 658 051 1153 2 j06 3 .4 -60 HBX-I 56.7 1.15 0 j083 - 0 3 9 6.42 055 1063 2.00 236 60-500 HBX-I** 56.1 137 0.066 - 0 3 6 6.15 055 1073 3.4-60 HBX-3 503 1.14 0.091 -0 3 1 6 633 050 905 2J02 543 1.16 0.091 -0 3 1 8 6.70 050 114.4 157 60-350 HBX-3** • •• • •• NOTE: All equations art of the form Parameter » K f>m ■ Peak Pressure (MPa) 0/W ,/3 - Reduced Time Constant (mt/kg, ', ) I/W ,/s « Reduced Impulse (kPa-sflcg,/1 ) E/Wl/* • Reduced Energy Flu* Density (m-kPa/kg1'* ) W - Charge Weight in Kilograms (kg) R - Slant Range in Meters (m) I and E are integrated to a time of 50 •Validity Range is range of the pressure (in MPa) over which the equations apply ••Equations arc based on limited dsts beyond about 130MPa, and should be used with caution •••Shock wave is not exponential, but has a hump; the similitude equation fils the portion of the wave beyond the hump. 142 where T is in seconds, W in pounds, and d in feet. According to Cole, (27), values of for cast TNT and PETN are 4.36 and 4.35, respectively. Figure 64 is a nomogram for determining the shock wave para meters of spherical TNT charges fired 1n deep water, (76). Figure 65 is a nomogram for the period and maximum radius of the fir s t bubble generated by a TNT explosion in deep water, (76). Results of underwater tests have been compared with various other tests and with rock blasting results. Atchison et. al., (24), compared underwater test parameters with strain measurements in granite rock for four explosives—one dynamite (HP-G) and three different grades of amnonium nitrate (N-IV, MN-M, MN-L) mixed with diesel o il. A typical strain pulse produced in rock and a typical shock pressure pulse produced in water are shown in Figure 6 6 . The events endure equally; the strain pulse is rounded because of absorp tion of high frequencies in rock. Also, the pressure pulse has a steep front indicating negligible energy absorption in water. The following pulse characteristics were evaluated from strain and pressure records: 1. The peak amplitude, 2. Impulse, which is proportional to area under the curve, and 3. Energy, which is proportional to the pulse squared. Appropriate scaling laws were used to remove the effect of charge size and distance. Table 15 shows relative values of these perfor mance parameters based on an HP-G value equal to 100. The following DISTANCE K M (INVERTED SCALE -USED IXS1ANCE. A ONLY EOA READING f l *“ L 2 100# -a PEarprESSURE.R #00 -H too —, (MR*) 70# MOO too too 300 ENERGY. E IMPULSE, I 4000 -a *#•■«) MOO -3 WO 100 7000 W H ______300 70 to .££■ ^ IlME CONSTANT.* too too 40 ~ (TIME CONSTANT TO BE RE AO too 300 30 JO N L V WITH INVERTED DISTANC1 30 700 3 SCALE! > 70 30 -5 / 300 to 300 40 100 BO BO 0J 30 to 40 BO 3 jO 40 40 h U M s» 70 30 >- BO 1.0 30 100 30 300 10 300 too !- too 700 0.1 — ' 0.7 o.t 1000 OS Figure 64 - Nomogram for Shock Wave Parameters for TNT (After Roth (76)). 144 w WEIGHT W«l A___ 10000 MAXIMUM RADIUS <*") ■000 ■000 SO —i 4 0 — 40 00 3000 30 3000 DEPTH (m) 1000 ■00 4.0 600 B.0 10 400 300 » 200 3 0 40 SO 60 ■0 100 4 0 30 200 20 3 0 0 ,400 X3 SOG .02 600 too 1000 ,006 .006 2 0 0 0 30 00 0 .1 0 .6 50 00 Figure 65 - Nomogram for Bubble Parameters for TNT (After Roth (76)). •»«» ~ H • W* n / » • ft M-Sd l»k Figure 6 6 - Typical Strain Wave and Pressure Pulse (After Atchison (7)). Table 15 - Comparison Between Underwater Tests and Rock Tests (After Atchison (7 )). M*ck u ttt h i k Strain Strain Crushed •tra in im pube volume HP-G 100 100 100 100 N-1V 70 n o II a MN-H 41 85 40 65 MN-L 41 69 26 57 \vcr»sc ituvdArd 15 11 50 15 error (percent) W attf tttn P m u n h c u u it Bubble preMura ompube enerjy «r*y HP-G 100 100 100 100 ^ •IV 102 19 99 10 «N-H M 76 56 77 S4N-L 42 49 23 31 (*tn |t titM iid 10 I 13 10 •nor (percent) conclusions were deduced: 1. Two methods gave similar rankings to the four explosives. 2. MN-L detonated at lower velocity 1n water than 1n rock due to confinement. 3. Peak strain differences between HP-G and the ammonium nitrates were larger in rock perhaps because of the d if f erences in impedance ratios between explosive-rock and explosive-water. Satyavratan and Vedam, (79). compared shock, bubble and total energies from underwater tests with lead block values for seven different explosives. They found a linear correlation between the underwater values and the lead block values, Figure 6 6 . The corre lation coefficient was 0.921 with shock energy, 0.930 with bubble energy, and 0.980 with total energy (shock plus bubble). Noren and Porter, (65) compared underwater Impulse and bubble energy with theoretical explosive energy and rock fragmentation in surface mines. Figure 67 confirms that a direct correlation exists between the measured underwater bubble energy and calculated explo sive expansion work. On the average, bubble energy for many d if f erent explosives was found to represent about 47.8% of the theoreti- , cal value. A similar relationship between measured impulse and cal culated explansion work 1s shown In Figure 6 8 . The test explosives for these results were of widely different compositions. Fragmenta tion measurements (using a photographic technique) in limestone and granite quarries with four different explosives Indicated that fragmentation does not necessarily increase with an Increase in 147 tr 01 t (««' 1JD W M no XD DO M JM J» ruuA UU OKI «uif (m /Uf I — ■ — Figure 67- Correlation Between Underwater Tests and Lead Block Tests (After Satyavatan (79)). •00 I HO 400 HD too *0 0 •oo woo uoo MOO Figure 6 8 - Bubble Energy Vs. Calculated Expansion Work (After Noren (65)). H 10 MifuH* • 304 .JOOOOSZ Uni I*. 04 400 400 •00 1 0 0 0 «00 MOO Figure 69- Impulse Vs. Calculated Expansion Work {After Noren (65)). 1 \ ' \ ”} limiilM | x i too too K>00 IOO ttOO IJ00 Figure 70 - Fragmentation Vs. Calculated Energy {After Noren (65)). explosive energy. Figure 69 shows the results. 149 Bjarnholt and Holmberg, (16), compared measured underwater expansion work calculated according to equation previously given for total expansion work and with computer code calculations of energy for many different explosives. Table 16 lis ts the composition of explosives tested, and Table 17 gives the calculated and measured values. The correlations were quite good for most of the explosives tested. To predict rock breaking performance of an explosive with reference to a standard explosive in bench blasting, Bjarnholt, (18), suggested the following equations: Equal weight comparison: (yEs + 0.6 Eb) (107) BP ’ (yEs + 0.6 EB)r Equal volume comparison: (108) where y is the shock loss factor defined earlier and pg is the 150 Table 16 - Explosive Compositions for the Tests (After Bjarnholt (18)). Oxyten Com position Dentit y Exploit vc Balance (Weight %> (g/em*) <%) Oxyyen Balanced CHNO Explotivci 4 JPETN/3 7AN/2Qlyeol h n tn tx 1.4 S -0.3 ISJHjO/O.SCuai ECDN 100ECDN 1.4 8 0.0 ANFO 94.6AN/5.4FO 0.90 0.1 Oxygen Deficient CHNO Exploited PETN 100PETN 1.00 -10.1 KMX I00HMX 1.20 -21.6 NM 100NM 1.13 -39.3 Hexotol 60/40 59RDX/40TNT/I Wax 1.69 -46.4 86PETN/I4FO 86PTTN/14FO 1.08 -57.4 TNT 100 TNT 1.58 -74.0 Alummiud Explosives ANFOAL 10 87.4AN/2.6FO/10AI 0.90 -0.5 MMAN acmit. wale (get WC 2 1.34 -0.3 expL 7 * At (60 Kin) MMAN ten lit. watcrgel WC4 1.36 -0.5 ex pi 136 A1 (60 uni) 42.IRDX/42.1TNT/0.8 He xo tonal 15 1.76 -56.3 Wax/I 5A1 <30 K m ) EGDN - Ethylene Clycol Dinitrate. MMAN-Mono Methyl Amine Nitrate. AN-Ammonium Nitrate Prill*. FO-Fuel Oil No. 1. 151 Table 17 - Measured and Calculated Explosive Energy (After Bjarnholt (18)). 1 > K > . C K a if t 4 - 0 1 1 ,1 4 - A l l ) F M l f l C l a t f . l i a t k O a t M l O n * * . I n L i k m . 1 * » F * s e w 5 fc * l W * 1 E i f l . i i * . W**CAI s n . f i * ; t w i n C M t i r K m . F i n * * ■ 1 I’KW r . M > C o O t «A«1 41. 11. 1. < C **> f *( ( M l/ O f ) f M l M t l o * r r m liM n l CIIMC I n K w n HL h i u . l 1 .1 3 C M • 5 1 .0 4 0.11 I.** 1)0 1.** 1.1* l .*0 4 . 0 0 4 0 L N . i i i .1 m D M . 1 1 1.00 0*1 I t * 1051 1 .0 3 3 0 1 3 * 0 4 0 0 OL h w . i 7.i* SM • 1) 1.00 0 ** U t n o 1 .0 3 XII i . t o 4 .0 0 701 ICON 0.1*1 C M * 11 1511 1*0 3 . 3 ) 1».) 1.01 1.** *.*0 •XI 7 0 ) r n r w 0 1*0 C m * i l 10) 1 4 3 3 .3 4 I*.l 3513 s.*t 0 .7 0 •XI 0 1 ANCO O J 4 0 L i t - t * 1 .0 1 0 X 3 3 0 1 3 0 1 X 5 XXI 1 .7 1 1 . 1 * 3 0 * X Oi l ANI'O LM C M * H 1 .0 1 0 * 1 3 -1 IX* 1 1 1 .7 1 IX* ML A N F C X 0 7 CM 1 .1 0 0*1 1 * 0 I X U t 1 .4 7 X T i IX* J 7 L A M H O M l C M * * 3 1.10 1.00 l . f l X ) U l 1 X 2 1 .7 1 XI* 1 X 7 4 I L A U F O 1 4 1 K M * 1 1 IOC * 0 3 1 .1 ) 3 0 1 X 5 XII XT* 4 I L AMFO 4 1 1 K M * M O 1510 1.0* XI* X) l i t 1 .3 7 1 .7 1 1 . 1 * « 4 l ANFO 10.01 S M * 1 4 0 1.410 1 .1 3 3 4 ) U 1 X 1 l i t 1 .7 * IX* 4 1 L AMFO *.*l KM • 11 1.00 O i l 1 X 3 i o 1 X 5 1 X 1 X 7 I 1. 1* O irp i DrfWwHi CI'UO liH « "n 7 3 5 FCTM 0 X 1 ) C M 1 .0 3 1 4 4 5 0 0 7 X to* 3X4 4.7* 4X1 301 I I M X 0 .1 4 0 E M * 4 1.01 1 4 0 3 . ) ) 1 ) 4 l . * 0 3.0* 3.7* 4.1* m MU 0 .1 * 4 C M - 1 0 1 .0 3 1 .1 4 XI) 1 1 X 1.04 4.4) 1.41 4 .1 1 3 5 ^ MraftM MW 0A K CM* 13 1511 1 . 1 * l o t 1 1 .1 3 X 5 4 . 1 * 4 .7 0 4 0 0 3 3 3 lifT T H il.F O 0. 1*1 C M * 11 1 5 )1 1.11 XI* IX 1.14 4 X 0 4 X 1 4 X 1 7 7 ) T U T 0 .3 1 5 1M * 3 i x n 1 .0 1 l o t III XM 4 .1 4 3 X 3 4 . * ) 4 L 7 M T t . * 7 SM* 1 150 O.fT XII l i * 3 . 0 * 4 0 * 4 .1 1 4 , » 1 1 TMT 4.** SM* 1 1.00 0 . * 1 X I ) 1 1 4 3 5 M 4 0 * 4 X 1 4 . * ) J 5 L TKT 1 * 4 0 4 * 1 0 1 .0 0 o . * o l . f l 10.0 3.CM 4 .1 1 5 X 1 4 , » ) AMfMnM* tlfllim 5 ) AMFOAL lO fV W 0 . M 4 C/4* I* 1.03 1 X 7 1 . * ) IO 1 X 5 4 0 1 4 4 ) 4 X 4 4 4 5 M a h FO a L l t d 1 0 ) 0 . 1 * 0 C M * I f 1 .0 ) 1 X 1 1 . * ) 351 IX) 4 0 1 4 0 * II AMFOAL 101*00) 0 ) 1 4 C M * 1 * 1 .0 1 1. 1) 1 .0 0 IO 1 X 5 4 . 1 * 4 4 ) J X * om AMFOAL 101*0* 1.10 CM* 140 1 .1 0 1 X 0 3 . 4 ) IX I X l 1 .0 0 4 4 5 4 X t IC W C 3 1 0 .1 1 C M * 1 * 0 1.00 1. 1) M i * 4 1 .1 0 4 .7 1 — 4 .7 1 01 w c * * . * 4 C M * M O 1.00 1. 1* 1.M1 * 4 1 0 5 5 4 * — * 0 7 7 5 5 I l H M W l 11 0.35) EM - 11 1.01 1 .1 5 3 . 0 * 1 1 .1 I X ) l o t 7 0 1 1 * 0 0 • M w u l* Nft. I. # • ■■ *«•««•*•• N*. I * ■ ftiw i*f fwewrd fkfw riiH , C jM itM C fe a lttlM t m f ) ) m m . 1S»**u «nh L ** P. «1«r» live* h m t N«. W f «M4 n 15 ■ !»«• ^ IT *C J « * > M t APPENDIX G STATISTICAL OUTPUTS 152 Table 18 - Peak Shock - Water Gel EXP 2 Fin TVX MUMPER OFODSFRVATTONS TN DATASET = 16 13:27 SATURDAY * MAY f J.9B7 3 GENERA1. LINEAR MODELS PROCEDURE DEPENDENTVARTADU■: pm SOURCE DF SUM OF SQUARES MEAN SQUARE F VALUE MODEL 3 402660.35410227 ,1 60HR6 , 70470076 4.56 ERROR 12 423332.32027274 35277.69335606 PR > F CORRECTEDTOTAL 15 905992.67437501 0.0236 R-SQUARE C.V. ROOT MSE PM MEAN 0.532742 21.9250 107.02356976 056.63125000 SOURCE DF TYPE I SS F VALUE PR > E EXP 1 22710.02562500 0.64 0.4379 DR 1 459020.31727499 13.03 0.0036 WT 0 0.00000000 ♦ * OR*EXP 1 122.011.20227 0.00 0.9541 WT*EXP 0 0 . 0 0 0 0 0 0 0 0 4 * DR*UT 0 0.00000000 • * DR*UT*EXP 0 0.00000000 4 t SOURCE DF TYPE ITT SS F VALUE PR > F EXF 0 0.00000000 4 4 DR 0 0 . 0 0 0 0 0 0 0 0 4 4 WT 0 0.00000000 4 4 DRKEXP 0 0.00000000 * » WT*EXP 0 0.00000000 4 4 DR* WT 0 0.00000000 4 4 DR*UT*EXF 0 0.00000000 4 4 Table 19 • Bubble Period - Water Gel rxp TUX mumper nr npsFRUATTQMstn data sft - s 14:or: Saturday. may 7 . 190 4 CFNERAL L TMFAR MODE! 5 FRnFFni IFF DEPENDENT MART APLF J TP SOURCE DF SUM OF SQUARES MEAN SQUARE VALUE MODEL 1 40.12961010 48. 17961818 0.73 ERROR 6 390.27330182 66 ♦ 37009697 PR > F CORRECTED TOTAL 7 446.30000000 0.4771 R-SQUARE C.V. ROOT MSF TFl MEAN 0.107820 4.4379 0.14603305 183. 57500000 SOURCE DF TYPE T SS FVALUE PR > F EXP 0 0.00000000 ♦ * DR 1 40.1296101B 0,73 0.4271 UT 0 0.00000000 • • DR#EXP 0 0.00000000 ♦ ♦ UT#EXP 0 0.00000000 • * DR#UT 0 0,00000000 * ♦ DR*UT*EXP 0 0.00000000 ♦ ♦ SOURCE DF TYPE TIT SS FVALUE PR > F EXP 0 0.00000000 • ♦ DR 0 0.00000000 » * UT 0 0.00000000 ♦ 4 DR*EXF 0 0.00000000 • 4 UT #EXP 0 0.00000000 t • DR#WT 0 0.00000000 • 4 PR*WT#FXP 0 0. 00000000 • 4 frSI Table 20 - Root-Mean Square Value - Shock Pulse - Water Gel FXP 1 TUX f JUMPER OF ntfSFR'JATinNS TN DATA SFT =>= 0 14! or: 5ATHRO A V . MAY 2r 1 9 H 7 R nniFRAi. l.thear nnriri s RRnrrruiRr: DEPENDENT VART ARI F J RMS SOURCE HF GUM OF GO! I ARES MEAN SRIIARE F VAI IJF MODEL 1. 8707*754P.776H 8787.25487368 17.97 i ERROR 3560.741 1 67,07 593.37357730 PR > F CORRECT Eli TOTAL 7 1.1 847.49878750 0.0097 R-SGUARE C.V. ROOT USE RMS MEAN 0.6994 94 9.1197 24.35925958 267.10675000 SOURCE DF TYPE I SS FUAL.ME PR > F EXP 0 0.00000000 « « HR 1 8707.25487368 13.97 0.0097 WT 0 0.00000000 0 * PR*EXP 0 0.00000000 0 * WT*EXP 0 0.00000000 * * PR*UT 0 0.00000000 ♦ * DRSWTfcEXP 0 0.00000000 4 ♦ SOURCE DF TYPE Til SS FVALUE PR > F EXP 0 0.00000000 * * DR 0 0.00000000 0 0 WT 0 0.00000000 0 0 DR*EXP 0 0.00000000 0 ♦ WT*EXP 0 0.00000000 • ♦ DR*WT 0 0.00000000 • 0 DR*UT*EXP 0 0.00000000 0 * Table 21 - Shock Loss Factor - Water Gel r xr 1 ivy numtifr nr-' nriSFRUATinrm in r«,'Ta set ~ a 14 105 5 ATURD AY . MAY 2 , 1 9 0 7 10 spheral lthfar nnnn s procedure dependent u a r ta d le : mu SOURCE DF SUM OF SQUARES MFAU SQUARE F VALUE MODEL 1 0.01 571564 0 . 01 5 71.5 A 4 1 .BO ERROR 6 0.0524043A 0. 0007473? PR > F CORRECTED TOTAL 7 0.06070000 0.2286 E-SQUARE C. V. ROOT HOF MU MEAN 0.230435 5.9954 0.09352750 1 ,56000000 SOURCE DF TYPE I 00 FUAL 1.1 F PR •- F EXP 0 0 . 0 0 0 0 0 0 0 0 ♦ 4 HR 1 0.01.571564 I. BO 0.2706 IJT 0 0 . 0 0 0 0 0 0 0 0 « 4 DR*EXP 0 0 . 0 0 0 0 0 0 0 0 4 4 WT*EXP 0 0 . 0 0 0 0 0 0 0 0 4 4 DR t IJT 0 0 . 0 0 0 0 0 0 0 0 4 4 DR*UT#EXP 0 0 . 0 0 0 0 0 0 0 0 4 4 SOURCE DF TYPE III SS FVALUE PR > F EXP 0 0 . 0 0 0 0 0 0 0 0 * 4 DR 0 0 . 0 0 0 0 0 0 0 0 * 4 UT 0 0 . 0 0 0 0 0 0 0 0 * 4 DR*EXP 0 0.00000000 * 4 WTKEXP 0 0 . 0 0 0 0 0 0 0 0 4 4 DR*WT 0 0.00000000 • * DR*UT*EXP 0 0,00000000 » 4 Cn cn Table 22 - Relative Bubble Energy - Water Gel F'T U’V MUMPER OF nTJPFR'v'ATTflN^ TM ft AT A SET ^ 8 1 4 JOG SAini 'MAV. MAY 7r GENERAL I IMEAR M OF FIG F'FOFFFUPF DEPENDENT VARIABLE: RTF SOI IRCF DF SUM OF SOUARES UPAM SQUARE F I ’,* M IF MODEL 1 0.008A2797 0.008A7797 0 . A A ERROR 6 0.0814 so nr. 0. 01 7.S71 81 PR > F CORRECTED TOTAL 7 0,0900SSS2 0.45SA R~SQUARE C.V. ROOT MSF PDF ME AN 0.090801 13.4429 0.1 1 A49811 0.8AAA17SO SOURCE DF TYPE I SS F VALUE PR > F EXP 0 0.00000000 * ♦ DR 1 0.008A2797 0.A 4 0.4SSA WT 0 0.00000000 * 4 DR*EXF' 0 0.00000000 f I WT * EXP 0 0.00000000 » 4 DR*WT 0 0.00000000 ♦ 4 DR*WT*EXP 0 0,00000000 4 « SOURCE DF TYPE III SS F VAI..UF PR F EXP 0 0.00000000 4 4 DR 0 0.00000000 4 4 WT 0 0.00000000 4 4 DR*EXP 0 0.00000000 4 4 WT*EXP 0 0.00000000 4 * DR*UT 0 0.00000000 ♦ ♦ DR*WT*EXP 0 0.00000000 * 4 tn Table 23 - Relative Shock Energy - Water Gel exp TV.' numrfr nr nnRrRVATiows tn t>ata rft - n 1.4 J 05 001110007 - MAY 2 * 19f17 16 GENERAL I TiJEAR nnnn s ppncFntiRF DEPENDENT VARIABLE! RSE SOURCE DF SUM OF SQUARES MEAN- 3PMARC F VALUE MODEL 1 0.19902403 0,199024R3 .1 7 7 .3 4 ERROR 6 0.00677370 0.001 1 777FI PR F CORRECTED TOTAL 7 0.20570073 0.0001 R-SGUARE c.v. ROOT USE RSE MEAN 0.967274 10.9070 0.03350070 0.30304900 SOURCE nr TYPE I OS F VALUE PR > F EXP 0 0.00000000 ♦ » DR 1 0.19907483 177,34 0.0001 UT 0 0.00000000 * * DR*EXP 0 0.00000000 4 • WT*EXP 0 0.00000000 4 * DR*UT 0 0.00000000 ♦ * PR#WT*EXP 0 0.00000000 ♦ ♦ SOURCE DF TYPE ITT SS F VALUE PR > F EXP 0 0. 00000000 • * DR 0 0 . 0 0 0 0 0 0 0 0 ♦ ♦ WT 0 0 . 0 0 0 0 0 0 0 0 « * DR*EXP 0 0 . 0 0 0 0 0 0 0 0 » * WTtEXP 0 0 . 0 0 0 0 0 0 0 0 4 « DR#UT 0 0 . 0 0 0 0 0 0 0 0 * 4 DR*WT#EXP 0 0,00000000 4 4 Table 24 - Modified Total Energy - Water Gel EXP TU\' mumper nr nnsERUATTOHstn fiat a set -- n , 141 OF RATI IRTlAY < MAY 7. GENERAL linear models rEnrEnupr DEPENDENTVARTable : nte SOURCE DF SUM nr SQUARES MEAN SQUARE r UAL I IF MODEL 1 07777.33OA0A7O 87777.330A8&70 20, OA ERROR A 10772.02390AA7 71 78, A70A51 1.1 p r > r CORRECTEDTOTAL. 7 10A549.35459700 O.OO10 R-SGUARE C.V. ROOT USE LITE MEAN 0.823319 9. 253A 55.934571 .10 r'.04.13307500 SOURCE DF TYRE I SS E VAI HE PR > E EXT* * 0 0 . 0 0 0 0 0 0 0 0 4 « DR 1. 87777.33OA0A2O 70.0A 0.0018 WT 0 0 . 0 0 0 0 0 0 0 0 » 4 DR#EXP 0 0 . 0 0 0 0 0 0 0 0 * 4 WT*EXP 0 0 . 0 0 0 0 0 0 0 0 ♦ 4 DR4WT 0 0 . 0 0 0 0 0 0 0 0 « 4 PR*UT*EXP 0 0 . 0 0 0 0 0 0 0 0 ♦ 4 SOURCE n r TYPE TIT SS F VALUE PR > F EXP 0 0 . 0 0 0 0 0 0 0 0 * ♦ DR 0 0.00000000 4 4 WT 0 0.00000000 » 4 DR*EXP 0 0.00000000 4 » WT fcEXP 0 0.00000000 4 4 DR#UT 0 0.00000000 « * DR*UT#EXF 0 0.00000000 4 • 159 < ♦ 00000000*0 0 dX3*in*ya < * 00000000*0 0 in*ya t « 00000000*0 0 dXJtifl « ♦ 00000000*0 0 dX3#ya * ♦ 00000000*0 0 in ♦ • 00000000*0 0 an « * 00000000*0 0 dXJ j < ad jn iyri j SS 111 J d U JII joanos « * 00000000*0 0 dX3*in*aa « ♦ 00000000*0 0 in*aa * * 00000000*0 0 dX3#in * * 00000000*0 0 dxj*ya * * 00000000*0 0 in *£60*0 Z6*Z frV£IEZ86*0fit'ddd I aa ♦ * 00000000*0 0 dXJ J < dJ jii ivn J Lid I Jd.U ja ooanos OOOOdii U*t'68 tr8a?£otu*9Ed 8UV"?o TZI8oE * 0 ijyjw wd 3sw ioua *0*0 jyynns-y VE60*0 ooos^B96*yfaEoi;s i—/ Tyioi ujiojaaoo j v y .j ZZiZddOO* 9tr09£ zzyzu to*yzdvu: 9 aoaa3 Z6*E tr9Z U8U6 * OM'Vil'ci, fc-VE tEdd6*0d^cdL; I 030 OK1 J in y n . jyyiiULi nvjw LiJdVlltJd JO Wild JII 3oanos wd :j iOVldVA IN3ON3dJO JdlHUJUdd S'lBPiUW dVJNl I IV>JJrJJ'J AVH * AVUaiUVLi LiOIft ‘J = IJLi V1VU Ml dNUilVniJJSdO JO yJONDif I.Jd dXJ a^LuieuAa - poqs - SZ Table 26 - Bubble Period - Dynamite rxr 1 r:n NIJMPER OP OPSERVATTONS 7N DATASET = 8 1 4JOS SATURDAYr MAY GENERALLINEAR MOnPIS PROCT DMRE DEPENDENT VAR IA PL,r: tp SOURCE nr sum nr souares MEAM SQUARE MOP EL i 60,39107773 60.79107773 ERROR 6 977.07777727 173.04628700 CORRECTED TOTAL 7 90S * 46877000 K-SQUARE C.V. ROOT MSP TP MEAN 0.061406 6.6762 12.40747006 107.10770000 SOURCE DF TYPE I SS E VALUE PR > P EXP 0 0.00000000 • 4 HR 1 60.79107277 0.39 0.7740 UT 0 0.00000000 * 4 DR*EXP 0 0.00000000 * 4 WT*EXP 0 0.00000000 * » DR#UT 0 0.00000000 » 4 DR*UT*EXP 0 0.00000000 « 4 SOURCE HP TYPE ITT SS P VALUE PR > P EXP 0 0.00000000 * * HR 0 0.00000000 * 4 WT 0 0. 00000000 « * HR*EXP 0 0.00000000 4 4 UT*EXP 0 0.00000000 • 4 DR*WT 0 0 . 0 0 0 0 0 0 0 0 + 4 DR*WT*EXP 0 0 . 0 0 0 0 0 0 0 0 ♦ 4 Table 27 - Root-Mean-Square Value - Shock Pulse - Dynamite EXP RI> MUMPER OFnDSERt'ATiriMS Til DATASET = 8 14105 SATURDAYr MAY 1 9 8 7 3 9 GEMERA1 L 7WEAR MODELS PROCFriiiPE DEPENDENTVAR 7aplej RMS SOURCE DF SUM OF SOtlARES MEANsniiARF F '.-'AI UF MODEL J 3A404.70AA1755 3A404.70661755 41 .51 ERROR 6 57A1.59013745 37A.9 3302791 pr > r CORRECTEDTOTAL 7 AT 6 A5.80 4 7 S0 00 0,0007 R-SGUARE C. V. ROOT USE RMS MEAN 0.87371? 10.3837 29.& 1305494 785.19750000 SOURCE DF TYPE I SS FVALUE PR > F EXE 0 0.00000000 ♦ DR 1 344 04. 20 A A 1.255 41.51. 0.0007 WT 0 0.00000000 * • DR*EXP 0 0.00000000 * ♦ WT#EXP 0 0.00000000 « 4 DR*WT 0 0.00000000 * • DR#UT*EXP 0 0.00000000 ♦ * SOURCE DF TYPE UT SS FVALUE PR > F EXP 0 0.00000000 + * DR 0 0.00000000 * 4 UT 0 0.00000000 ♦ 4 PR*EXP 0 0.00000000 * 4 WT*EXF 0 0.00000000 4 4 DR*UT 0 0.00000000 • 4 OR#UT*EXP 0 0.00000000 ♦ 4 Table 23 - Shock Loss Factor - Dynamite FXP 1 F.Ti NUMBER n r MtSFRUATTnNS TN DATA RET = B 14105 SATURDAY, HAY GENERAL LINEAR MODELS PROFFnURF DEPENDENTvariable : MU SOURCE DF ’>UM OF SO HARES MEAN SOUARE MODEL 1 0.00777314 0.00777314 ERROR 6 0 * 00601.43A 0.00100739 CORRECTEDTOTAL 7 0.OOB73750 R-SQUARE C.V. ROOT HSF MU MEAN 0.315577 1.7951 0.031AA0A1 1.76375000 SOURCE DF TYPE I SS FVALUE PR > F EXP 0 0.00000000 « DR 1 0.00777314 7 77 0.1473 WT 0 0.00000000 * PR*EXP 0 0.00000000 * WT*EXP 0 0.00000000 DR*UT 0 0.00000000 * DR*UT#EXP 0 0.00000000 SOURCE DF TYPE ITT SS FVAIHE PR > F EXP 0 0.00000000 ♦ DR 0 0.00000000 « WT 0 0.00000000 « DR*EXP 0 0.00000000 WT*£XP 0 0.00000000 ♦ DR*UT 0 0,00000000 * DR#UT*EXP 0 0.00000000 ♦ Table 29 - Relative Bubble Energy - Dynamite EXP Rfi NUMBER OF ODSERVATIDNS TN DATA OFT =* 0 14105 SATURDAY!. MAY 3 * 1.'? 0 7 45 GENERAL LINEAR MODELS PROCEDURE DEPENDENT VARIABLE; RDF SOURCE DF SUM OF SQUARES MEAN SQUARE E VALUE MODEL 1 0.00753605 0.00753605 0.30 ERROR 6 0.15300325 0.02550054 PR > F CORRECTED TOTAL 7 0.16053930 0 . AOA3 R-SQUARE C.V. ROOT MSE RDE MEAN 0.046942 19.5025 0.159A888? 0.SIRS1375 SOURCE DF TYPE I SS F VALUE PR > F EXP 0 0.00000000 ♦ DR 1 0.00753605 0 30 0.6063 WT 0 0.00000000 t DR*EXP 0 0.00000000 4 UT*EXP 0 0.00000000 • DR*UT 0 0.00000000 ♦ DR#WT#EXF 0 0,00000000 • SOURCE DF TYPE III SS F VAII.JE PR > F EXP 0 0.00000000 • DR 0 0.00000000 ♦ WT 0 0.00000000 4 DR*EXP 0 0.00000000 * WTfEXP 0 0.00000000 4 DR*UT 0 0.00000000 4 DR*UT*EXP 0 0 . 0 0 0 0 0 0 0 0 4 Table 30 - Relative Shock Energy - Dynamite EXP rri NUMBER nr OBSERVATIONS TNBATA BET R 141 Of SATURDAY * MAY P.t 1 ?R7 47 DEPENDENT OAR T ADI.e: rse SOURCE nr SUM nr SQUARES MEAN SOUARE E VAI..LIE MODEL l 0.17943A7B 0. 1.7943A73 1 .in. 94 ERROR A 0.0092061 A 0.001547/,9 p r > r CORRECTEDTOTAL 7 0..10072294 o .o o o i R-SQUARE C. V. ROOT MSE RSE MEAN 0.950795 12.9901 0,03934074 0.50285237 SOURCE DF TYPE T SO F VAI UE PR > F EXP 0 0 . 0 0 0 0 0 0 0 0 4 DR 1 0.17945A 73 11594 0.0001 WT 0 0,00000000 4 DR*EXP 0 0 . 0 0 0 0 0 0 0 0 4 UT*EXP 0 0 . 0 0 0 0 0 0 0 0 4 DR*WT 0 0 . 0 0 0 0 0 0 0 0 4 DR*UT*EXP 0 0 . 0 0 0 0 0 0 0 0 4 SOURCE DF TYPE III SS F VAI.ME PR > F EXP 0 0.00000000 * DR 0 0,00000000 4 WT 0 0 . 0 0 0 0 0 0 0 0 4 DR*EXP 0 0,00000000 4 UT*EXP 0 0 . 0 0 0 0 0 0 0 0 4 DR*UT 0 0 . 0 0 0 0 0 0 0 0 4 DR*UT*EXF 0 0 . 0 0 0 0 0 0 0 0 4 Table 31 - Modified Total Energy - Dynamite exp 1 Rn MUMPER OF OBSERVATIONS TN RATA SET = 0 14105 SATURDAY ? MAY GENERAL 1.1 NEAR MODELS PROCEDURE DEPENDENTvariable : MTE source DF SUM OF SQUARES MEAN SQUARE MODEL 1 375A2.95422145 375A2.954 221.45 ERROR A 45A97.04320055 7414.17386676 CORRECTEDTOTAL 7 03259.99742200 R-SQUARE C.V. ROOT MSE MTE MEAN 0 * 451152 15.0725 07.270A930A 579.00500000 SOURCE DF TYPE I SS F- VALUE PR > F EXP 0 0.00000000 4 4 DR 1 375A2.95422145 4.93 0,0681 WT 0 0.00000000 4 4 HR*EXP 0 0,00000000 4 4 UT*EXP 0 0.00000000 4 4 DR*WT*EXP 0 0,00000000 4 4 DR*U1T 0 0.00000000 4 4 SOURCE DF TYPE III SS E VALUE PR > F EXP 0 0 . 0 0 0 0 0 0 0 0 * 4 DR 0 0.00000000 4 4 UT 0 0.00000000 4 4 DR*EXP 0 0 . 0 0 0 0 0 0 0 0 4 4 WT*EXP 0 0.00000000 4 4 DR*UT*EXP 0 0.00000000 4 4 DR#UT 0 0.00000000 4 4 APPENDIX H CALCULATION OF EXPLOSION PRESSURE 167 168 APPENDIX H CALCULATION OF EXPLOSION PRESSURE Explosive: PETN 3 Density: 1.6 g/cm (average) Molecular Weight: 316.2 Reaction Products fo r Unbalanced Oxygen State: (109) C5 H8 ^N03^4 4H2° + 2N2 + 3C02 + 2C0 Reactants Grams C = 5 x 12.01 = 60.05 H = 8 x 1.01 = 8.08 N = 4 x 14.01 = 56.04 0 =12 x 16.00 = 192.00 316.17 Heat of Formation for Reactants, Qp = 123.0 Products Grains (mole) kcal H20 = 4 x 18.02 72.08 -68.4 x 4 -276.6 N2 = 2 x 28.02 56.04 0 x 2 0 .0 C02 = 3 x 44.01 132.03 -94.1 x 3 -282.3 CO = 2 x 28.01 56.17 -2 6 .4 x 2 - 52.8 TT 316.17 -608.7 169 Heat of Explosion ■ Qe « Qp - Qr (110) * -608.7 - (-123.0) « -485.5 kcal/mole * -485.7 v 1______T 0.3162 kg/mole = -1536 kcal/kg Explosive State Temperature = i*e * M ^ C r y ) i + Ti1 (111) where Te = explosion temp., °K = moles of product/kg of explosive Cv = average heat capacity kcal/mole - °K o. Tj *= in itial temperature of explosive (25 c) Assume T = 4800°K e Products n-± K " i Cv h 2o 12.65 10.001 126.51 n2 6.33 6.550 41.44 C02 9.49 12.347 117.16 CO 6.33 6.602 41.76 326.87 Te • tllla^kc^l^kg - ~ ° e * * W ° K 170 * 4997°K T\ - 4997°K e Explosion Pressure ■ Pg ( 112) where Pg - explosion pressure (atm) ng = total moles of gaseous products (moles/kg) = 11/.3162 ■ 3.479 moles/kg R = gas constant * 0.08206 liters - atm/mole - °K V0 = sp ecific volume o f gases (lite r s /k g ) Because the volume 1s assumed to remain unchanged during the explosion, the density of the products w ill equal the explosive's original density. Therefore, V - — . p e The co-volume factors which correct gas volume at high pressures for the significant volume occupied by the molecules themselves were taken from the tables (15). The gas volume generated by the explosive is assumed to be much larger than the borehole in which it is contained, therefore, no sig nificant heat loss results from expansion. The borehole volumes were calculated: V = ttA (113) where V * volume o f borehole (cm ) r ** radius of borehole (cm) h * depth of borehole (cm) 171 Approximation of reduced temperatures for gaseous products may be found as follow s: Mole C ritic a l Tr Tr Product Fraction Temp. °K Product Fraction h 2o 0.363 647 7.7 2.80 n2 0.182 126 39.7 7.22 C02 0.273 304 16.4 4.48 CO 0.132 133 37.6 6.84 1 .0 0 0 21.34 The critical temperatures (T ) can be found 1n the Introduction to Chemical Engineering Thermodynamics by Smith, 0. M ., Van Ness, H. D. The reduced temperature is Te/Tc. Tr = Zl The explosive borehole pressure * P (114) where Z ■ average com pressibility o f gaseous mixture n = moles/gr of explosive T * Te V - volume o f borehole in lite r s p . Z(0,;.0246)[0.08206)1M00). for J/16. hole where P - 50 57 Z atm * 74338 Z psi 172 Gases compared at their reduced temperatures and pressures display nearly the same compressibility factors and they all seem to deviate from their Ideal behavior to the same degree. Assume P «* 95,000 psi C ritic a l Fraction Pressure Prod. pr H20 0.363 3205 1163.4 N2 0,182 493 89,7 C02 0.273 1072 292.6 CO 0.182 507 92.3 1638 r. j „ Assumed Pressure Reduced Pressure, Pr = ------1535------(115) For Tr = 21 and Pr Go to compressibility chart to find Z then Z (74338) e P. Repeat until assumed P equals calculated P, Pr = TO T = 57 •997558 A = 1.324 P = 1,324 (74338) » 98481.96581 Assume 99000 Pr « 60.439 Z » 1.338 P <= 99498 Assume 99668 PR ■= 60.8 Z - 1.34 P = 99668 P « 99668 APPENDIX I ENERGY - BREAKAGE CORRELATION 174 175 APPENDIX I ENERGY - BREAKAGE CORRELATION To show that the measured values of breakage from a previous study correlated with the measured energy releases In this study, distrib u tio n s were made and the slopes of the plotted curves were compared. Since relative bubble energy (RBE) and relative shock energy (RSE) were measured 1n th is study and breakage was measured 1n the oth er, a common facto r must be found. Both cases can be compared to pressure. Since industry-wide, all explosives are related to TNT, the detonation and explosion pressures for TNT were used to predict pressures for shock energy and bubble energy respectively. Therefore, the follow ing equations were used: Shock Pressure = SE = Pg (RSE) (116) where P^ ~ Detonation Pressure (Cook (31)) Bubble Pressure = BE = Pg (RBE) (117) where Pg = Explosion Pressure (Cook (3 1)) The values may be found in Table 32. The breakage versus pressure values were obtained from earlier research, Britton (21). These values also appear in Table 32. Table 32 - Breakage - Pressure Correlation Data Breakac e Shock Pressure Bubble Pressure W2 Grams W2 Atm Atm 13.0 375 16.0 12411 16.0 18084 31.5 479 38.6 22173 38.6 21115 50.0 510 61.4 46179 61.4 26027 68.5 520 84.0 53703 84.0 26484 87.0 576 177 A Welbull distribution was used to demonstrate this correlation. Since the data points for SE and BE were four and the breakage data had only five points, the following relationships were used to yield the Wei bull percentages. W% distribution = 2. - 0.3 / 4.4; i = 1,2,3,4 (118) and W% distribution - Zi - 0.3 / 5.4; i = 1,2,3,4,5 (119) where 1s the Y value of a particular data point. The X values are breakage and pressure where Xj < Xg < ••• < X^. The slope of each curve was given by: N * (In In (pjU - In In / In (X2 / Xj) (120) where N = slope of curve If the slope of SE and/or BE lies between the Gaussian slope of 3.33 and the Wetbull slope for breakage (BR), then the point is proven. That 1s, the correlation has been substantiated. From Figure 71, the following values were obtained: NBR = ^ln 1n (r ^ 9 > " ln ln ^l-.027^ ^ 1n ^300^ Nbr =6.4 approximately 6 NfiE = (ln In - In In / In (||) NfiE =5.9 approximately 6 ^SE ~ - In In (y_|jjj)) / ln (^-) “ 1*3 Bubble Pressure Slope a G 5hock Pressure Slope = 1J Grams (10?) figure 71 - W Versus Breakage-Pressure CO 179 It can be seen that breakage and bubble energy correlate very well while shock energy does not. It should be noted that more data points would have been better, but at the time of the testing, we were Interested in the close range of applicable decoupling ratios. BIBLIOGRAPHY Ash, R.L., "Drill Pattern and Initiation-Timing Relationships for M ultipie-H ole B lastin g," Colorado School of Mines Q uarterly, Vol. 56, No. 1, (January, 1961). Ash, R.L., "The Mechanics of Rock Breakage," Parts I through IV, Pit and Quarry. 2 through 5 (August through November, 1963). Ash, R.L., "Rock Breakage by Explosives," Emphasis on Blasting, Ed. J. H. Dannenberg, Vol. 9, No. 4, (December, 1973), and Vol. 10, No. 1, (March, 1974). Ash, R.L., "The Influence of Geological Discontinuities on Rock Blasting," Ph.D. Dissertation, Univ. of Minnesota, (1973). Ash, R.L., Konya, C.J., and Rollins, R.R., "Enhancement Effects from Simultaneously Fixed Explosive Charges," Transactions of the Society of Mining Engineers/AIME, Vol. 224, (December, 1967). 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