COUPLING RELATIONS IN BLASTING

By

Muhammad As 1am

A thesis submitted to the Facu1ty of Graduate Studies

and Research in partial fu1fi1ment of the requirements

for the degree of Iv1.aster of Engineering

Department of Mining Engi.neering and App1ied Geophysics,

McGi11 University, Montreal.

May, 1966.

CD Muhammad As 1am 1967 (Copy I)

(

ABSTRACT

This investigation explores the mechanics of transier oi

energy from an explosive to a hard rock. The response of two very strong

rocks (Q > 25,000 psi) magtletite and quartzite to a shock wave (plane) u

generated by the detonation. of pcntolitc (a high velo city explosive) has been

studied. The results are described in terms oi peak pressure versus dia-

tance, peak pressure versus compressibility, maximum partide velocity

versus distance and shock propagation velocity ve l'BUS distance.

In the magnetite and the quartzite both maximum partic1e :"

velocity and peak stress close-in to the explosion point attenuated expenen-

tially. The decay in maximum partic1e velocity in these teot mate rials ia

m~re pronounced at high stress levels, while the attenuation in the peak

atreas i8 greater at lower stress levels.

A comparison oi the detonation pres sure obtained (in the

present study) on the basls' of acoustic theo1'Y of coupling with the known,

(thermohydrodynamical) methods shows that the acoustic theo1'Y of coupling

applies fairly closely fo! estimating the transfer of explosive energy to

theso rocks.

, .

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ACKNOWLEDGEMENTS

1 am deeply indebted to Dr. D. F. Coates for guiding me in

analytical rock mechanics studies in general and shock wave studies in

particular. My horizon ovel' the subject has been widened through the

opportunity of working in the atmosphere of Mines Branch, which has been

possible through the generous arrangements approved by the Directo~p

Dr. J. Convey.

Sincere thanks to Professor R. G. K. Morrison p Chairman

of the Department of Mining Engineering and Applied Geophysics, McGill

, . University, for intl'oducing me to theoretical rock mechanics and for

suggestions fOl' improvement of this research report.

The work for this pl'ogram has been carried out with the hclp

of the following individuals:

D.A. B. Stevenson: Idndly made available the facilities of

the Explosive Reseal'ch Laboratory •

. G. Larocque, _K. Sassa, R. Pal'sons p J.A. Darling: helpful

discussion and suggestions. In addition J.A~ Darling supervised the use

of explosive.

D.E. Gill (McGill University): introduced me to the various

laboratory techniques dealing with the aubject.

Fo Kapeller, S.R. Cook, J. Sullivan, C.S. Szombathy:

extended theh' ingeniou6 sleiU in aU phases of the project.

- iii -

The Iron Ore Company of Canada cooperated by Bupplying the

rock blocka.

In the laat, special thanks to Mll"o Paul Larsen for his

meaningful suggestions and general help.

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- iv -

CONTENTS

Abstract •..•.. • • • • • • • 0 • • • • • • • • • • • • • • •

Acknowledgements • • • • • • • • • • • • • • • • • • • • 0 • •

Introduction . . ,. Il " • • • • • • • • • • • • • fi • • • • • • • • • • •

Statement of the Problem · . . . . . . . . . . . . . . .. . . . . . . . Previous Work on Shock Transmission . . . . . . . . . . . . . . . Method of Approach . • • • • • • • • • • • • CI U • • • • • • • •

Theory ••• . . Experiment •.

Experimental Procedures ,. . . . . . . . . '" . . . Shock Propagation Velocity, CL Preparation of Rock Plates •• Explosive Description Shooting Assembly

Results and Discussion ..•.• . . . . . . . . . . . . "

i

ii

1

2

4

18

18 23

28

29 29 31 31

40

Shock Velocity Measurements •. , • . . . . • . • . .• 40 Comparison of the Theoretical Seismic Propagation

Velocity with the Measured Shock Propagation Veloc ity . . . • • . . • • • . • • • • • • 46

Maximum Partic1e Velo city • • . • 52 Peak Stress ... ~ . • . • • 52 Percentage Possible Error. . . . • • • • 55 Method of Evaluation of the Variables and Their

Er1·0rs .. 0 • • . •• III 0 ••

Coupling Relations • • • • • • • • • GOInpres sibility u • •

58 59 64

CONTENTS (Continued)

Physical Properties of the Test Rocks. . .

Conclusions

References

Purpose •••• Approach Testing •••• Pre-Failure Characteristics . Failure Characteristics ••

. . .

. .. . . . . . . . . . . . .

.. ')

Appendix - Uniaxial Compression Test Data. Creep and Plastic Strain Data Brazilian Test Data

Conversation Tables . . . .

. . . . . . .

67

67 67 67 69 69

72

74

77 79 80

81

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No.

1.

2.

3.

4.

5.

6.

7.

8.

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FIGURES

Expected Stress Wave Shape •••.

Expected Displacement Time Curve •

General Experimental Arrangement

An Example of Gap Distance vs Time Plot (Magnetite Plate 13.00 mm Thick) •

Rock Plates

Detonation Velocities of Pentolite Explosive

Pin Circuit • • . . . • • • • • .

An Exmuple of an Oscillogram.

• • 0 D • • • • 0

. . .

• • • tI

9(a). Propagation Time vs Distance from EJcplosion Point for Pentolite-Quartzite Coupling ••...•.••••.••

9(b). Propagation Velo city vs Distance from Explosion Point for

Page

16

16

24

25

32

34

36

37

41

for Pentolite-Quartzite Coupling . • • • • • • • . . • • 42

10(a). Propagation Time vs Distance from Explosion Point for Pen tolite -Magnetite Coupling. • • • . . • • • . • • • •

10(b). Propagation Velocity vs Distance from EJeplosion Point for

43

Pentolite-Magnetite Coupling. . . • • . . • • • • • . . • •• 44

11. Compressibility vs Stress fol' Quartzite. 45

12. Maximum Particle Velocity vs Distance for Pentolite-Quartzite Coupling • • . . • • • . • . • • • • • -. • • 53

13. Maximum Partic1e Velocity vs Distance for Pentolite-Magnetite Coupling . . . • • • • • • • . • • • • • Ct Ct • 54

14. Peak Stress vs Scaled Distance 60

15. Peak Stress vs Distance fol' Pentolite-Quartzite Coupling 61 l'

16. Peale Stress vs Distance fo:!' Pentolite-Magnetite Coupling 62

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FIGURES (Continued)

No. Page

17. Comprcssibility vs Stress for Magnetite ••••••• . . . . . 66

18. Typical Stress-Strain Diagram of the Various Rocks Te B ted. . . . . CI • • • • 0 • • • • • • Il • • • • • • . . . . . 71

TABLES

1. Magnetite-Pentolite Pin-Contact Plate Experiment Data 49

2. Quartzite-Pentolite Pin-Contact Plate Expel'iment Data 51

3. Phyaical Properties of the Rocka CI'OO'O.OOOODOOÙ 68

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INTRODUCTION

A blasting research project was initiated in 1963 in the

Mining Research Laboratories, Mines Branch, in Ottawa. The ultimate

objectives of this program are ta prcdict the fracture boundaries in hard

rocks from explosions.

During the first phase of this project the pin-contact te<:h­

nique was used to atudy,in the laboratory,shock transmission from high

velocity pentolite and 10w velocity Belite A 60% explosives in a very strong

magnetite. On the basis of the laboratory findings, data were obtained on

the coupling of the explosives \vith the magnetite, the attenuatiol1 of the

peak stress in magnetite and the variation of rock compl'essibility with the

stress.

The present investigation ia an extension of the laboratory

part of a continuing project and is an attempt to irnprove the existing tech­

nique. Special attention was given to sorne of the uncertainties in deter­

rnining the shock wave velocity in previouseJCperiments D in which two very

strong rocks (rnagnetite and quartzite) were subjected to a shock from

pentol~~e expl?sive.

o (

o

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s'rATEMENT OF THE PROBLEM

In physico and variouB branches of engineering, coupling ia

defined as an interaction between systems or properties of a system. For

blasting in boreholes Duvall (14) defined coupling as the ratio of charge

diameter to the borehole diameter. Cook (9) has presented the idea of

ahock coupling, which ia Bubatantially as uaed below, and energy coupling.

Hia definition of energy coupling ia quite aimilar to Duvall'e definition of

borehole coupling.

The "coupling" in thia work ia defined aa the"ratio of the

transmitted pressure to the detonation pressure. Numerically, this ratio

will be des.fgnated a.s the coupling factor. The coupling factor will be pl'e-

dicted by using the acouat:l.c theory:

= Eq. (1)

(where Pt ia the transmitted pressure in the rock at the interface with the

explosive, Pd ia the d~,tonation pressurej) CL ia the shock propagation

velocity, D ia the detonation velocity, p is the eJcplosive density and p ia e

the rock dena~tyo)

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)

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With the coupling factor obtained from the acoustic equation

a.nd the trallsmitted pressure, Pt obtained from the measurement of den-

fJity, P , propagation velocity, CL' and partic1e velocity, v, the detonation

pressure, Pd' in the explosive can be calculated. A comparison of the

detonation pl'CtHlUre, Pd" wlth the detonation pres Bures obtained directly (8)

from the thermohydrodynamic Eq. (2) can give sorne idea of the validity ai

the acoustic theory of coupling at high pressures.

The thermohydrodynamic equatioll can be expressed as:

Eq. (2)

where Pz V 2 and T2

i8 the pressure, volume and tempe rature behind the

wave-front. The factor a. (V Z) is essentially an erroI' factor, which is

l'equired to take into accound the expected error in V 2 at high pressures.

a. (V2

) can further be expressed in terms of another factor, known as 13 V 2 - a. (V 2)

factor through the relationship: 13 = V 1 - V 2

In view of so many approximations (31, 32, 34, 35, 36) which

have been applied in the derivation of Eq. (2), and the fact that 13 can be

determined only to within 5 pel' cent error (from measured detonation

velocities accurate to within 2 to 3 pel' cent), some of the authorities (8)

are satisfied using the following approximate equatioJ;l:

pl/-

2 = 0.00987 P eD'" ~. 380-12 70p e) Dll-p

c Eq. (3)

- 4 -

where P2

is the pressure in atmospheres, D is the detonation velocity in

rn/sec (Pentolite = 7730 rn/sec), p ia equal to 1.722 g/cc, P is the c e

density of the explosive (Pentolite = 1. 65 g/cc) and the symbol represents

the ideal quantity.

PREVIOUS WORK ON SHOCK TRANSMISSION

Free Surface Velocity Technique. To utilize explosive energy

more efficiently, it is necessary to understand, how the energy is trans-

ferred to the rock. Many researchers both in the field of luetallurgy and

rock rnechanics have studied this transient phenomenon and have attempted

to devise relationships concerning energy transfer on the basis of the pro-

perties of the explosive and of the solid invoived. This has normally involved

an attempt by sorne experimental means of determining the detonation pro-

perties of the explosive and the equation of state of the metal or rocle mate rial.

Plane shocle waves are invariably used.

Duvall (14) ln 1960 measured a pres sure of 348 le-bars in

aluminum just at the interface of aluminum and COluposition B explosive.

In this experiment he used piezoelectric probes to record the arrivaI time

of the shock waves. In this way, he could measure the shock propagation

velocity. The probe introduced into the specimen due to its different

physical properties from the specimen may act as an undesirable acoustic

- 5 -

boundary. Hence, the use of the probes is liable to introduce a serious

(\1'1'01' in velocity measurements. Nevertheless, the r~sults indicate that

the detonation pressure for Composition B calculated on the basis of acouatic

theory (307 k-bars) differa less than 15 pel' cent from the thermodynamic

method (C-J pressure = 270 k-bars). Any such comparison was omitted by

the author.

Minshall (21) in the same year l'eported thf:1 results of his

studies with iron alloys, which involved shock propagation d.nà free surface

velocity rneasurements. A target plate-pin contact experiment was used

to deterluine the free surface motions imparted by various explosives. A

transmitted pressure (Pt) of 228 k-bars (for Armco Iron and high explosive)

was measured. Due to unknown explosive details, it is difficult to say

whether the acoustic theory applies to this experiment. However, the author

recognized the serious error which may result from the indirect deter­

mination of shock propagation velocity if the fl'ee surface motion is not Imown.

In this work, the shock propagation velocity is detel'mined by dividing plate

thiclmes s with intercept t:i.rne. The intercept time is ohtained by extra­

polating the displacement versus time curve to zero displacement. If this

curve is not completely defined an error mal' occur iri. intercept time.

CuI'l'an (10) studied the attenuation of the shock wave in

aluminum by stl'ildng aluminurn flyer plates upon alnminmn tal'gets and

measuring the tal'get fl'ee surface velo city as a function of target thiclmes s.

\

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The results from this experimental study disagree with the prediction of

hydrodynamic theory exhibiting premature attenuation. The measured free

surface velocities were considerably Iower than the predictcd free surface

velocities from hydrodynamic theory. AU the conceivable systematic

cxpel"imental en'ors (cdge affecta, oblique gcomch'y" spallation of' target

face, spallation of flyer face} which could give rise to premature attenuation

were climinated. To explain the disagreement in the results an elastic-

plastic model was proposed.

Depoigny and SchaH (11) used X-rays and radiographs for the

mcasurement of shock propagation and free surface vc1ocities. For aluminurn,p

the X-ray technique indicates a lower transmitted prcssure, (P ) compared t

r) to a frce-surface velo city method (21). The exact reason for this differcnce

is not lmown; however, it is mentioned here that the donor and receptor

technique (1) also indicates lower pressures (as compared to free -surface

velocity method) for rocks.

The description of the. iwo· methods (free-surface vclocity

method, and donor and receptor technique) is as foHows. In the free-surface

velo city method of pressure measurements g a stress wave(longitudinal) is

transmitted through the material (solid). The stress "Yave on strildng the

free-surface of the mate rial i.mparts a motion to it which can be measured

with the use of electrical methods (e" g., pin-contact technique g piezoelectric

probes 3 papel' insulation spacers)~ The free-surface displacement is then

-) p10tted against Ume and the maximum s10pe of this curve gives the maximum

frce - surface velo city ~ which 18 taken as e:lcactly twice the particle vc10city p v 0

- 7 -

The time for cOlnputing the stress wave propagation velocity, CL' is also

obtain6d from the free-surface dis placement versus time Cl.lTve. From the

known maximum partic1e velocity~ v, stress wave propagation velocity, C , L

and mas s dens ity, p, the peak pre s sure transmitted to the mate rial is com-

puted from Eq. (6).

Donor and Receptor Technique. In the donor and receptor

technique, the solid mate rial (known as the barrier) is placed between the

two charges, one of which is known as the donor and the other as the receptor.

When the donor charge is initiated. a detonation wave is produced. The

detonation wave after running the donor charge length reaches the donor barriel.'

interface. At this interface, a, stress wave is transmitted into the barrier.

Within the barrier, the stress wave attenuates in intensity. A portion of

the stress wave at the end of the barrier thickness (barrier-receptor inter-

face) enters into the receptor charge. The balance is reflected back into the

barrier lTIaterial from barrier-receptor interface. In the receptor charge,

the stress wave if of Gufficient intensity will initiate its detonation after

travelling through a finite distance, d. Otherwise, it will further attenuate

just like its attenuation in any other solide This phenomenan of initiation in

the receptor charge is the most important aspect of the donor receptor tech-

nique. The finite distance, d, and detonation velocity, D, in the receptor charge

is determined with a high speed streak camera. From an extensive invest­

igation (1), the relationship D ::: 5.5 e -dl 10 + 2.5 (for Composition B-3 and

spessarite) has hecn estabHshed where D is in rnrn/jJ. sec and d is in mm.

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From the known detonation velocity, D, and explosive density,

P e' the trauf:lmitted pressure (= Pt_r' in the receptor charge) is calculated

from the thermohydrodynamic method (Eq. 11). A curve of transmitted

pressure (= P in the receptor charge) versus initiation distance, d, is t-r

plotted. For Composition B-3 and spessarite combination, the relationship

Pt = 181 e -d/7. 5 + 21 has been established (where P is in k-bars and -r· . t-r

d is in mm). The transmitted pressure (in the receptor charge) versus

initiation distance, d, is then extrapolatcd to zero initiation distance to

dctermine the transmitted pressure at the receptor-barrier interface. From

the known transmitted pressure (= P D in the receptor chàrge), explosive t-r

density (P e) and dctonation velo~ity.? D (in the reccptor charge) the incident

pressure (P.) in the barrier matcriaJ. at barrier-rcceptor intedace is calcu­l

lated frOlu the acoustic expres sion namely:

P . =~ e D + P b CL-.2:>~p

i 2 p D t-r e

where Pb is the barrier rnass density and CL

_b

is the stress wave propagation

velo city in the barrier"

But in this equation,? CL

_b

is still unknown~ which can be

determined as follows:

t = t '1- t t b r

where t is time taken for the shock transmis sion in the barrie r to travers e t

the barrier as well as the initiation distance» d 3 into the receptor; tb

is the

transit time in the barrie},' mate rial alone and t is transit time in the reccptor r

charge.

- 9 -

Time tt ean be directly measured from photographie recorda

d a~d tr is caleulated from tr = D' therefore, t

b = tt .. tr can be found. Now,

if Tb ia the barrier thiekness and CL

_b

is the average stress propagation

velocity in the barrier, then

=

Further, if partic1e velocity, Yb' in the barrier material

ia desired (for eompariaon purpoaes) it can be determined from Eq. (6):

P. l

It ia difficult to say with certainty which of the three tech-

niques ia m.ore accurate.

To investigate the compressional behaviour of x-cuts y-eut

and z-cut quartz cryatals and fused quartz at high pressure ranges (up to

750 le-bars>, produced b}r the detonation of explosives Wacherlc (29) applied

the high speed optical technique. In both varieties of silica two wave struc-

tures over a wide pressure range were identified. The first wave indicated

lower free-surface velocities « 1 mm/f.L-sec) than the second wave (> 2mm/

p.-sec). The sequence of variation of free-surface velo city with time i6 that

the velocity riaes from 0 to 0.8 mm/f.L-see during 4. z' - 4025 p.-sec interval.

During 4.25 to 4.50 f.L-sec interval, the velocity decreases to 0.75 mm/f.L-sec.

At 4.5 J..L-,see time, the velocity again l'iaes to greater th an 2" 1 mm/J..L-sec.

In Wacherle's opinion, the second jump in the free~aurface velocity ia an

indication of the fluid-like bchaviour of the mate rial rather than elastic.

- 10 -

o A reasonable description of the mechanics of this transitlOn (from elastic

)

to fluid), however, requires further insight into the phenomena. Correlation

between the detonation pressure with the transmitted pressure (in quartz)

was omitted.

Work by Shreffler and Deal (26) dcmonstrated that when

a thin metal plate is accelerated by an explosive system through a few centi­

mctres before maldng an impact on the stationary brass plate. considcrably

higher local energies can be obtained. A photographic technique was applied

to mcasure the metal free-surface velocity, and a mcthod for reducing the

photographie. data was citcd~ The study was l'estrictcd only to frce-surface

velocity mcasul'cments p Detailed analysis of the free-surface motion \Vas

omittec1. To explore this fUI'ther, McQueen and Marsh (22) carried out an

extensive investigation on 19 metala (Ag. Au, Cd, Co, Cr, Cu, Mo, Ni" Pb,

Sn, Th, Ti, Tl. Vs W, Zn, Bi. Fe" Sb). The photographic flash gap tcch­

n1...]ue was applied for the measurements of the velocities associated with

the plane stress waves. Shock pressures obtained from the impact of the

accelerated driver plate with a stationary target plate were found to be

approximatp.l)' thl'ce times the original shoc1c pressures in the cll'iv,.:l' plclLe.

Walsh and Rice (30) detonated high explosives to transmit

shock wavcs through the metal plate and into the liquid which is in COlltilct

with the opposite surface of the metaL A movil1.g image camera was uscd

to mea[;ure the velocities aS80ciated with the shock waves" The pressure

range in 15 liquids (watel'3 mercurY3 ethanol, methanol, hexanc 3 carbon

disulfuide, mono nitro toluene. t01uene, N-amyl alcohol, ethyl ethC1'3

- 11 -

o acetone, bromomcthanc, glycerine, carbon tetrachloride, benzenc) was

found to be {rom 50-150 k-bars. No attempt to explain the mechanics of

transfer of explosive energy from explosive to liquid was made. Only

Hugoniot curvcs (transmitted pressure versus relative volume) for thcse

\

)

liquids WCl'e studicd.

Contcmporarily in the field of rock mechanics, !to,

Terada and Sakurai (18) published the results of their joint study on the

"stress waves in rocks and their cffects on rock breakage". ln their study,

concrete mOl'tar, marble and sandstone were the various rock substances

which were subjected to Sakura dynamite, Shinkiri dynamite and Muraski

carlite. In order to measure the free-surface luotion of these specimens,

paper insul;;ltion spacers were inserted betwccn a lead block (which was

us ed as one clectrode) and the tin foil cemented on the undersurface of the

specimen. They found that with the combination of Shinkiri dynamite and

marble 3 shock propagation velocity increased with distance from the explo­

sive rock interface for 30 mm, and beyond this distance a graduaI decrease

followed.. The authors attributed this increase in shock propagation velocity

(with distance !rom explosion point) to the generation of a plastic wave of

higher order near the explosion point" It was presumed that the gcneration

of the plastic wave is due to partial decomposition oi' marble at extremely

high temperatures (tempe rature in. the wave front) and shattering into very

fine pieces duc to sudden decrease in temperatul'e (due to stress l'elease)u

The concept of the plastic wave is still controversial o

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- 12 -

Atchison and Tournay (2B) measured the peak strain and

the Bize of the. crushed zone in a granite (Q = 30,000 psi and p = 164 lb/ft3

) u

produced by different explos~veB. The results indicate that both peak strain

and size of crushed zone have a good correlation with the detonation. pl'eStmre.

The crushod zone volume. however. was not as sonsitive to vadD,1:ion in

detonation pressures as was peak strain. The possibility of error in deter-

mining the exact crushed zone volume, however" was recognizedby t,he

authors.

Fowles (15) in 1964 obtained the Hugoniot data in the

pressure range 40 to 500 le-bars fol' poxous playa from the·' Nevada Test Site ..

Both in-contact and flyer-plate explosive arxangements were used. Below

240 k-bars p' the in-contact arrangement was used. In this arrangement

an explosive pad is placed on one side of the aluminum plate (lmown as the

drivex). The playa samples were mounted on the opposite side. The

detonation in the explosive produces a stress wave in the aluminum plate,

which;l in turng produces a sh'ess wave in the playa. Stress waves of

various pressures are obtained by using different explosives.

To obtain pressu ree (transmitted) above 240 k-bars in

the playa, a similar axrangement is used except that the stress wave is

pxoduced in the aluminum plate by impact fl"om a steel plate. The 1/B in.

thick steel plate (lmown as flyer plate) is accelel'ated by the explosive gases

and after a flight of 1i in, through air it strikes the alurninUlTI plate and induces

a shock into it,

- 13 -

It may bc mentioned here that in this experiment the free­

surface velocity measurement l contrary to Wachedefs (29) measurements,

shoy/ed no evidence of multiple wave structurc.

So far very Httle is known about how the transfer of

energy takes place (or how the coupling is affected) when a third matcrial is

used between the rock and explosive~ This aspect of the energ}' transfer has

a special importance because in almost aU mining blasting~ paper-wrapped

explosive cartridges are used and also sorne air is always present between

the explosive cartridge and the waHs of the borehole. Charles (4) in his

Ph. D. thesis (1963-64) developed a pellet technique and stildied the varia­

tions in shock decay with sever.al materials (water~ drilling mud» marblc,

alUlninull1, .plcxiglass a vermiculite, sand, ca.rdboa.rd, foam s rubber, air)

placed between the pentolite explosive and the Yule marble. Among these

materialo he found that ahock deca,Y (fol' the samo thicknooo) io tho highoot

in air and lowest in water.

~ellet Technique. In the pellet technique, the explosive

and the pellet (uflually of the sarne mate rial as that of the plate) are placed

on the opposite sides of the plate (oi the material under study). Thc

detonation in the explosive produces a compressivc stress wave in the plate.

The compressive stress wave aiter travelling through the plate enters the

pellet on the opposite side of the plate. At the free-surface of the pellet,

the compressive stress wave is reflected as a tension wave, and when this

tension wave l'caches the plate-pellet inte:dace, the pellet scparates and

flics away from the plate. The velocity imparted to the pellet by the stress

I)

- 14 -

wave is deterrnined by photographing a reference grid beforehand and then

stroboscopically photographing the flying pellet without advancing the film.

From the measured velo city, the pellet momentum per unit area is calcu-

lated~ The slope of a curve of pellet momentum per unit area versus time

gives directly the stress transmitted acr088 the plate-pellet interface into

the pellet because the stress or force per unit area is proportional to the

time rate of change of mOluentum per unit area.

The technique is open to an objection. Due to the Hnite

rise time of the peak stress (Figure 2), t11.e1'e ie the probability that the

pellet may detach from the rock specimen before the stress attains its peak ..

1 However" the author (on the basis of the breaking by reflected tension theory)

daims that, the pellet will remain in contact with the rock for a time interval,

f:::.. ' '_ 2 (pellet thicknes s) t - shock propagation velocity •

If this relationship is true then the stress

is expected to attain its peak before the pellet is detached from the plate

because the time for minimum pellet thickness 0.06 in. and shock propagation

velocity 5500 mis is 0" 57 fJ.-sec which is iar greater than the expected rise

time « 0.2 p_-sec) of the stress {1B}"

Towards the middle of 1964:1 SaF.>sa and Coates (7) released

a blasting research report under the tille "Stress Waves Close-In fron1

Surface Explosions". In this investigation they used a pin-contact techniqu'3

(described in detai! in subsequent pages) to measure the free-:-surface Inotion

of the test specimen. The frce -surface vclocity mcaSUl-ements with the pin-

contact technique may bccome difficult in cases of porous rocks (lilce scoria).

- 15 -

.0 The various combinations of rock and explosive j,n thi6 investigation were

aluminum-pentolite p magnetite-pentolite and magnetite-Belite A 60%. The

rC6u1ts of this study showed that the attenuation in the peak-stress against

distance at high stress levels (in magnetite) is lower than its attenuation at

\ lowor S11-008 levels, the acouotic theory of coupling may Biva a lair pro-

diction of transmitted stress, and change in variation of compressibility

with stress in the magnetite occurs at a stress level above 150 k-bars.

Subsequently, in 1965, they conducted field investigations

(6) in the same rock (magnetite), which gave a further insight into the

possible use of the acoustic approximation.

Austin (1) in 1965 used the donor and receptor technique

) to study coupling relationships. In his opinion the assumption (which ia used

in the pin-contact technique) that particle velocity in the incident stres s wave

(v.) and in the reflected stres a wave (v ) is the same is not true for aH the l r

solids o To emphasize his point a little further, he derived the following

equation:

Eq. (4) V r = ~ vi :20 «: -::~Ii

where v. is the particle velo city in the incident stres s wave, v is the l l'

pilrticle velocity in the reflected stress wave, Po is the initial virgil1 material

del1sity, P2 is the final shocked material density and Plis the density of the

material during compression.

)

-0 L

~" \ )

)

U) U)

w a: t­U)

t­Z W ~ W U .q:

- 16 -

TIME

Figure 1. Expected Stress Wave Shape.

...J il.

~J TIME

Figure 2. Expected Displacement Time Curve.

- 17 -

Austin' s (1) interpretation of tais equation is that if

po=pzthenv =~v.andvf =v.+v =Zv., wherevf

isthefree-r 1 s 1 r 1 s

surface velocity. The equation Po = Pz is true for most of the metals

with about 1 pel' cent error resulting from inadiabatic shock com-

pression. But it is not true that Po = Pz in case of brittle mate rials

like rocks. Porous rocks like scoria will increase while dense rocks

lilce diorite will decrease in. density after they are exposed to shock.

As a contrast between the two techniques, he found that

for a particular cOlnbination of explosive and rock the pin-contact

technique gives higher values of transmitted pres sure than the donor

and receptor technique.

)

- 18 ..

METHOD OF APPROACH

Theo2}:"

When an e,xplosive charge is detonated in a rock substance~

stress waves are generatcd. This description is restricted only to the

peak radial stresses in the stress waves. The stress wave is simply a band

in which the rock substance is subjected to longitudinal compression •. In

[l'ont of the band and behind the band, the rock substance is not compresHcd ..

At any particular moment, the new mate rial in front of this band is just about

to be compressed while at the same time mate rial bchind this band is de­

compressing. The stress wave while traversing through a rock substance

imparts a motion to the individual partic1es, V 3 {compression and decomp­

ression} which ie relatively amall compa1I'ed to the stress wave (longitudii1al)

velo city •

When the stres s wave is incident normal to the free sUl'f~ce,

the compressive wave is refiected as a tensile wave (17) and vice versa.

For this work it is assumed that wh en the remains of the incident wave

meets with its reflected portion, it cancels the stresses and doubles the

particle velocityo For example, if we take two squarewaves, onc of them

compressive and the other tensile, approaching each other the resultant

stress and the particle velocity in the region of interference of the two

waves can be obtained by applying the principle of superposition. If a, and

aZ

are the stresses, equal in magnitude, in the compressive and tensùe

S:':l'ess wavco respectively, -Chen the resultant stress in the area of illi;c;',

- 19 -

C) ference will be CT l = (Jl-(J2 = O. Similarly, if vi and v2

are the resu tant

partic1e velocities in the two waves, then the resultant particle velocity

will be v resultant = v 1 + v2 = 2v (v 1 = v2 = v).

Wh en the incid.~nce of the wave is not normal to the ü'ee-

surface both reflected shear and longitudinal waves (25) are produced and

these cancellations and amplifications bccome more complexa Further

complications are added due to the reflcctions from the structuraI and

texturaI discontinuities in the rocle substance.

The peak radial stress in the stress wave attenuates with

distance from the explosion point. The attcnuation is mainly due to 10ss

of energy in crushing, geometrical divergence and partial reflections al

acoustic boundaries and friction losscs in the rock. The crushing (2, 1i)

of the rock substance takes place when the peak radial stress in the stress

wave exceeds the dynamic compressive strength of the rocle. AIso, whon

the wave is reflected frOlu a free surface and the net stres s at the front

of the reflected wave exceeds the dynamic tcnsile strength of the rock.

To estimate the radial stress distribution as a function of

position <1Hel timc, the following simplified stress analysis (27) for thc

directly projected longitudinal wave generated from a spherical charge i8

presented. The rock mass for this analysis has been assUlued as semi-

infinite, isotropie elastic solid. However .. in view of the pas sible stru.ctlual

and texturaI discontinuities in the racle ma.ss and deviation of the properties

of the racle substance from a perfectly elastic solid, the l'esuUs of the

analysis must be used with caution.

C)

\

- 20 -

Let us assume the centre of the sphel'ical charge aa the

origin of a spherical coordinate (1', 0, Y;) in an elastic" homogeneous and

infinite medium of density po At any arbitral'Y point in the medium, the

radial stress component of the directly projected longitudinal wave is given

by the equation:

(J :: (À + 2~) 81' + À(80

+ 8y;) Eq. (i) r

where è)U

r 8 ::

d7 r

1 aUa U :::-ea = dO + r r

1 dUyJ Uo U r

e91

= ayr~ + cot 0 +-ï sin a r r

whcl'C Ur' Ue~ Uf& = displa.cemel~t8 i~l the l', 0, % dh'ectiona caused by

the longitudinal wave and can be expressed as:

U :: Uer, 7. ) r lp

whcre

'( ip

:: t r

t :: time from the instant of c1etonation

r :: distance from the origin of coordinatcs

C :: propagation vclocity of the longi.tüui\~;.ll L

wavc in the rncdiunl

À~ p. :: Lanléls const.Jntf;.

- 21 -

, When we substitute the values of 8 r' 8

0, ,8 pf in Eq. (i) we

get

Cl = (À + 2J.l) ~U (r, T. )./- 2À U (rl' T. ) r. or lp r lp

Eq. (ii)

As the displacement changes with Ume, the radial displace-

ment Uer, T. ) can be indicated by the product of U (r) and U (T. )~ where lp p w Ip

U (1') is a function of rand determines the peak value of the displacement, p

and U (T.') is a function of T. and indicates the wave shape or change in w IP IP

displacement with time ll namely:

U = Uer, T. ) = U (1') U (T. ) r IP p w IP

differentiating Eq. (Hi), we get

dU (l', 'r. ) lp -a-l'-- =

dU (1')

g. - Tl (T. ) + W lp

dU (T. ) W Ip

cl T. " 11'

Eq. (Hi)

Now the rate of change in the radial displacement with time

is the partic1e velo city, v(r:l T. ). Ip

Therefore dU(T. ) dU (T. ) dT.

ver, T. ) = IP = w lp Ip

U (1') Ip dt dT. x ""â"t p

Ip Eq. (v)

and also

dT. 1 .2..) Ip (T. = t -ar =

CL Ip CL

dT. Ip dt = 1

- 22 -

By substituting the values from Eq. (v) and Eq. (vi) in

Eq. (iv) we get

dU(r,T.) Ip

::

dU (1') P

dl' U (T. ) -

W 1P

v(r,T. ) Ip

Eq. (vii)

Substituting the values from Eq. (vii) in Eq. (ii) we get

{

dU (1') ver, T.)} U(r,T.) . (J :: (À +2!J.) d P U (T. ) - C lp + 2À 1~ Eq •. (viii)

. l' l' W 1P L l'

But À + 2J.l.

P

Suhstituting the valuc of (À + 2J.l.) in Eq. (viii) wc get

(J :: pC a p U (T. ) {

dU (1')

r L dl' w 1P __ -=Ip,-- + 2À . Ip Eq. (5) ver, T. )} Uer; T. )

CL r

In this equation, s inc e we do not Imow the function U (T. ) W 1P

and U (l'), it cannot be applied directly to the present pin contact plate p

cxpe:;:iment. To estimate the peak radial stresses in the experiment, the

gellerated shock wave is assumed to be plane and Eqe (6) has been used.

The assumption that the shock wave is plane near the explosion point is

l'easonably true (4,7, 14) as the wave originating !rom a colurnn cnargd

is fairly flat (plane) near the explosion point. The details of geometry of

the colurnn charge are described in subsequent pages.

Incidentally if the functionsU {T. } élnd U (1') arc ignol'.-:t' in w 1:-" p

Eq. (5)~ the remaining equaHon i8 the sar.oc as Bq. (6).

\

-'\

)

- 23 -

Expe l'iment

In previous investigations (7)1 SOlbe difficalty was experienced

in measuring the shock propagation velocity in the vicinity of the explosive.

It was thus dcsirable to m,odify the existing technique. Experimenta were

to be made on a magnetite and a quartzite to compare the magnetite data

with él; second hard rock.

The following modüications for the technique were made:

(a) The usual surface displacement venms time curve is

as shown in Figure 2. In previous tests (7), the minimum distance beLween

the undersurface and the first pin (Figure 3) was 0.005 in. This distance

accms to be too great to determine accuratcly the intercept time (Figure 4)

. . .. plate thickness for calculatlOns of ahock propagatlOn veloClty ( = . .-). As the

, 1l1.tcrcept tllne

firflt pin is placed doser to the bottom sudace of the 7;Oc!" specimcll b , thel·c

is the possibility that point a (Figure 4) will ahift to the left. Accordingly~

the first pin was set as close to the undersurface as pos sible. The brass

pins sharp tip results in the productiorl of a high electric field. When the

voltage gradient exceedl?_ the breakdown strength of the air between the tip

and the paint~ partial ionization of air takes place. This "Corona effectIf

restrictcd this ai-rangement 50 that 0.002 in. was found to be the safest and

closest distance.. The displacenlCnt ver s'us time curve could have beeu

better defined if one could use more than three pins. With the p:..·osent.

recording unito the miniU"lUm tin10 which ean be obtained beLwecn the tirnc

marks of 3/8 ino length ia 0.5 micToseeonds and for sueh a large tin1.c it

, , ,

) SPECIMEN

)

- 24 -

DETONATOI~ - . iON GAP WIRE 2I1iooo") (ENAMELLED

~~_",'~_=oJ ~-

®

®

TRIGGER

No.:

Figure 3. O rnent . . l Arrang. • cdmenta General Exp

--' ..J

~."

LO~-

0.8

-E E _ 0.6

1 IJJ u Z

~ tf)

ëi Cl.. OA'-« (,!)

0.2,-

.0' . L 21'4 2.5 2.6 2.7 2.8 2.9 3.0

Figure 4.

rIME (/,-5)

An Exainple of Gap Distance vs Time Plot . (Magnetite Plate 13. 00 mm Thick).

---------------.-----------,.----,-,c---

t"- '.f'\ ~: J

N U1

- 26 -

is not possible to get distinct blips (due to·overlapping of the blips) for a

spacing less than 0.015 in. between con ecutive pins for 1/4 in. and 1/2 in.

thick plates and 0.012 in. for 3/4 in. and 1 in. thick plates.

(b) At the interface of the .explosive pellet and rock plate,

\ due to the finite thickness ( ~ 0.021 in.) of the enamelled wi1'C which is used

as an ion gap (Figure 3), an air gap may occur. To reduce the stress

attenuation, the air gap was previously filled with plastic. explosive (7).

This type of filling improve s the expe riment, but it doe s not produce id,eal

coupling between the explosive and the rock. The gap may not be completely

filled with plastic explosive. Also. some mismatch betweèn the plastic

\O!xplosive with that of the pellet explosive occurs.

In order to achieve beUer coupling between the explosive and

the rock in t.his experiment, a silver conducting paint of negligible thickness

was applied to the rock surface. ,Another feature of this paint is that one can

solder a phono-pickup wire to it directly. The contact between the solder and

the paint is very· delicate so that the contact sometimes breaks in the handling

of the assembly. To overcome this vexation, a brass foil can be used to make

more than one contact and the phono-pickup wire can be soldered over the

brass foil. The whole contact may be covered with a masldng tape to pre-

vent breaks. Insulation of more th an one megohma the Ininimull1 l'equircd

[or the existing labo:ratory electronic circuitry to avoid pre-detonation short

circuiting. can be produced by leaving the air gap in the silvel' conducting

- 27 -

(c) The aluminum foil and Araldite on the bottom surface

was eliminated. In previous worl< (7), the aluminum foil on the under~

surface (Figure 3) of the rock specimen added to the thickness of the rock

plate from 0.002 in. to 0.005 in., which is undesirable for both surface and

shocl<: propagation vôlocity monaurcmente. lu the cace of tbin rock platos,

the inf1uen~e of the foil and cement becomes even more important. To

eliminate both cement and aluminum foil, the conducting layer of small

thickness was produced with silver paint.

(d) The stress wave may not move exactly normal to the

bottom surface (13).. The exact reason for this tilt of the ~vave front is

difficult to determine. It seems probable that this happens only when the

) undersurface of the rock plate is not perfectly plane. With the existing

means it is by chance that one achieves a perfectly plane rock surface;

however, to get close to a perfect~y plane surface l rock plates having

more than 0.0005 in. difference in thickness in the are a of the pin circ1e

(Figure 3) wel'e discarded. To measure the magnitude of the tilt, the

three pins Wel"C placed at the same gap distance from the undersurface of

the plate and arrivaI Lime of the free surface was measured in a series of

tests.. ln these tests no difference in arrivai time was found ..

- 28 -

EXPERIMENTAL PROCEDURES

The expected stress versus time relationship (7) is shown in

Figure 1. The interest in the present investigation is mainly in the fiat

portion of the curve, where the stress attains its peak and hecomes indepen-

dent of time.

The studies are restricted to plane stress waves. The peak'

stress normal to the wave-front (19) is given by the equation:

a = pCv x L

Eq. (6)

where a is peak stress normal to the wave-front, p is n1ass density, C i6 x L

shock propagation velocity and v is rnaximum particle velocity.

To avoid any distortion in the plane (stress) wave due to edge

effects, the lateral dimension of the rock plate should be larger th an its '

thickness. An estimate of the minimum possible width to thickness ratio (22)

can he made from the following equation:

Eq. (7)

where w is width of rock plate, t is thickness of rock plate, C is sound

velocity, CL is shock propagation velocity. and ,P s is the ratio of densities p

across the shock front and can be calculated from the Eq. (8) conservation

of mass (12) in shock transition:

, 1

C":) 1

,-;

- 29 -

1 Eq. (8) =

where v is particle velo city •

The assurnptions on which ;Eq. (7) is based have not been

specified by the author. Using the appt'oximation (Eq. (7»), the value : = 2.5 " p

is saie for making velocity measurements for compression with""":: as high p

as 1.6. T"he charge should be aligned with the centre of the rock plates.

Shock Propagation Velocity, CL

One method (25) of computing the stress wavc" velocity is to

substitute the elastic constants in the following equations:

or

3k(1-v) P (1+)1) =

E(1-v) p(1+v)(1-2v)

(when v = 0.5)

Eq. (9)

Eq. (10)

whcrc CL is longitudinal velo city of stress wave~ k is bulk modulus, p is

mass èlensity and v is Poissonrs ratio of the rock. But at high stress levels~

these cOluputations may involve error due to the variation in k. p and v at

these stres s levels a Experimental measurements (CL) have thus been us cd.

Mean CL was obtained by dividing the plate thickness (Figure 3) by the intcr­

cept tirne (Figure 4).

Preparation of Rock Plates

Massive blocks of two vaôeties of magnetite (A" B) and one

variety of quartzite were selected from formations at Wabush, Labl'"do;:'.

,

!;

- 30 -

n J

In both magnetite and quartzite the banding was quite pronounced and the

cores were drilled perpendicular to banding planes only. This was done to

eliminate the variable of banding, which was expected to have Borne effect

on the coupling of rock with explosive. These cores were then s1iced with

a diamond saw into plates of various thicknesses ranging from 1/4 ino to

1 1/4 in. thick. The rock plates were then c1eaned, measured and checked

for flaws. The geological description (24) of these rocks (Figure 5) is as

follows.

Magnetite A (Magnetite-specularite) is similar to type B

(described bclow) but has been stru.cturally deformed (Figure S(a)). Breccia

fragments up to 1 cm diameter and flow features are evident. Bands of

r-) large grai~ed quartz and specularite occur. The specularitc is often pre-

sent as blade-like inclusions in the quartz~ Type Aa in gencral has a higher

silica content than type B.

Magnetite B (Specularite -magnetite) is a fine-grained mixture

of specular hcmatite, quartz and magnetite (Figure 5(b)}. The specularitc

and magnetite vary in their relative percentages but are together more

abundant than the quartz. Thin section analysis shows the silica to be in

anhedral interlocking grains with an average diameter of O. 1 mm (24).

The specularite is mainly elongated subhedral crystals with an average

length of 0.5 mm. The magnetite grains are mainly anhedral and of the

same dimensions a.s the quartz.

)

- 31 -

Quartzite is a very pure coarsc graineçl silica rock. The

grain aize averages '2 mm. The texture can be clearly seen in Figure S(c).

A thin discontinuous 1ayering can be acen perpendicu1ar to the surface of the

disc, consisting of iron oxides.

~xplosive Description

Pentolite is the on1y explosive which was used for this experi-

ment. It is composed of two components in the proportion PETN:TNT::60:40.

Mechanically it falls in the category of high detonation ve10city explosives.

It has a density of 1. 65 g/cc, a detonation velocity of 7730 m/s, and the

reported (8) detonation pressure according to Eq. (2) of 220 kg/cmt:. The

ballistic mortar power for pentolite is 127 per cent.

Along with Hs high deî:onation velo city, pentolitc has one of the

smallesî: critical diameters for detonation in an unconfined charge, and it

can readily be cast into required sizes and shapes, which is most desirable

ior fundamental investigations. A cylindrical column charge (1 7/16 in.

diameter and 1i in. height), which is shown in Figure 3, was foul1d to be

the most suitable al"rangement for this experiment. Pentolite is cap sensi-

tive. but to achieve its perfect detonation tetryl boosters (1S g pellet) were

used.

Shooting Assembly

The shooting assembly is as shown in Figure 3. The top

pellet of the explosive has been used for two reasons: to allow sorne dis-

tance to build a constant detonation velocity (Figure 6) and to eliminate any

erroi" wh.ich could occur in 'detonation veloci:ty due to sweep dclay tirnc of

1 , . \

\

/' ,'",',

/ .. '

l' , : ~. . .

,': . l' ','-, j' ,

\, l, l'

" ,

\:

\ \

'. \ \.

- 32 -

.. ~-' . : '~1-" ~ ":.' :: ;"'~',_ . • ~,~, ': :=,,:..,. l~ .... 1 ',::' " '-..

'. "

" 1

,,' ,

" "'

5(a) Spccularite -Magnetite Ore Type A

'\ ,

'.' , .1."

','. " .l.··

" ,

/ ..

" .(, .

',\, .. :'.'

~ .. \

\ \

1 1--- .'-

, ,

1 J, :

. , /: . :

, l,

) 1 ,'-._-~-*'

,.~---.... . '

1

5(b) Specularite-Magnetite Ore Type B

Figure 5. Rock Plates.

[) ,~

":J!...'

)

1 1 i

1

" \

1

\ 1

i : 1

) 1

1

, ,

, "l'"

- 33 -

! ' 1

, 1

1

.. '.' ....

i ,1

1 : '

5(c) Quartzite

- 34 -

x:LO

600 o.

'"" III , E

0 ..... r t: u 700 0 ...l lI./ > Z 0 1-<~

600 z 0 l-l!.! Cl

._)

500-

400-------,------------~,-------------------~L-------==---------o 2 4 6 6 10

DISTANCE FROM IN\11AïrON (cm)

l!"igure 6. Detonation Velocities of Pentolite Explosive.

- 35 -

the oscill0scope. The signaIs at the trigger and No. 1 ion gap (Figure 3)

were made by twisting enamelled wire (O. OZ1 in. diameter) and cutting at

the end to produce a tiny ion gap (resistance > 1 megohm). This end of the

wire is adjusted approximately at the axis of the explosive pellet. Alter

the detonation is initiated. ionized gases arc produced which due to their

conducting property short circuit this ion gap and in this way the arrivaI

time of the detonation wave at No. 1 ion gap is indicated in the form of a

blip on the oscilloscope sweep whïch has already been started by the short

circuiting of the upper trigger ion gap. Exactly the same thing happens at

No. Z ion gap, the only difference being that at this level ihs'tead of enamelled

wire, silver conducting paint has been used.

The arrival time of the undersurface of the rock plate at the

vai"ious pins below the undersurface is also indicated by the blips whcn the

silver conducting paint at the unde,rsurface touches the pins. A simple pin

circuit is shown in Figure 7. The source voltage charges a smaU capacitor

through a resistance RZ (RZ > R 1)3 and when the pin is grolmdcd, the capacitor

is discharged through the resistance Il 1 and a pulse voltage is developed and

a blip appears. The rcco:rding apparatus consisted or an oscilloscope and

a zig zag unit~ and the sweep was photographed by using polaroid films. The

zig zag trace was used for extending the time axis Q A 'typical oscillogram

has been shown in Figure 8.

Th th b "(F" 3) d eacll at 1200

e 'ree ras s plns • 19ure wer? arrange

on a circle of 6 0 35 mm radius concentric with thd charge axis. This lateral

separation of the pins was such that the impact at one pin should not influc.:cc

/1') ,

)

- 36 -

10 PiN

Figure 7.

T }.;,.-_--i'''-( ~

j ro OSCillOSCOPE )-

r1

Pin Circuit ..

-------------_ ... - .

- 37 -

Figure .. B. An Example of an Oscillogram.

)

r)

)

- 38 -

the free-surface velo city at a neighbouring pin. The expected surface dia-

placement versus time curve is as shown in Figure 2. The maximum slope

of this curve represents the maximum free-surface velo city which is taken

as exactly twice the maximum particle velocity in the incident stress wave.

Taldng into consideration the wavc shape, the thicknes s of the

plate and approximately the magnitude of the maximum surface velocity;

these pins are then adjusted close to the undersurface of the rock plate so

that only the free-surface velo city of the plate is measured rather than the

velocity when the plate becomes a projectile_ A pos sible uncertainty exista

in the true time of pin c10sure due to the presence of high ~'electric field at

the sharp tip of the brass pin.When the free-sruface is just approaching

the pin, the small air gap between the pin and the surface is ionized and

the condenser (Figure 7) starts discharging through resistance R 1- This is

why the blips in the oscillogram (Figure 8) are not sharp. This may be

more significant in the case of thicker test plates (1 in. or more) where the

surface velocity is relatively low. The alternative to this method (pin­

contact) is the capacitance gauge but it may aiso be influenced by the noise

(electro-magnetic waves) accompanied with the detonation o

Aiter firing a first few shots, the following gap distances

we1:e found to be the most appropriate"

- 39 -

/~) Thickness (in.) of the Distance (in.) from undel'surface plate of the plate

1st pin 2nd pin 3rd pin

0.25 0.002 0.017 0.032

0.50 0.002 0.017 0.032

0.75 0.002 0.012 0.022

1.00 0.002 0.010 0.018

Realizing the need for precise measurements of these gap

distances a microscope was tried but due to roughness of the surface of the

pins, the microscope could not l'esolve more than O. 0005 in~ 1 therefore,

a dial gauge (0.0001 in.) mounted OIl a tripocl with a magne tic base was

") found to be. equally accurate and more convcnient.

)

- 40 -

RESULTS AND DISCUSSION

Shock Velocity Measurements

The experilnental data for both magnetite and quartzite obtained

from the pin- contact plate cxperilnents have been tabulated in Tables 1 and 2.

Due to the dispersion of data, it was difficult to differentiate between the two

varieties of magnetite (A and B), so they have been combined.

To obtain the stress wave propagation velocity corresponding to

those points where maxilnum partic1e velocity was measured, the following

procedure was used. The stress-wave propagation tilnes obtained from the

oscillograms (Figure 8, for various plate thiclmesses) were plotted against

distances (Figures 9(a) and 10(a». The slopes at various points along the

curve were .taken as the propagation velocities at those points. The pro­

pagation velocities thus obtained were plotted against dist::lnce (Figures 9(b)

and 10(b», and from this curve the propagation velocity was obtained at the

desired intermediate points corresponding to the points where the maximum

partic1e velocity was lueasured.

From the shock propagation velo city versus distance curve

(Figures 9(b) and 10(b}} 'for both quartzite and magnetite, it appears that during

the first 10 mm of the travel of the shock wave from the explos ion point, the

propagation velo city increases very rapidly, and after attaining its peak at

10 mm it falls gradually with f:urther ü·avel. This peculiar characteristic

of shock propagation velocity in these rocles lS quite different from metals (1.3)

and is presumably due to the relatively higher compressibility (Figures 11 and 17)

which these rocks undergo above a certain stress level (abovc 110 le-bars in

quartzite and 160 k-bars in magnetite).

U il> ID 1 :t

il> :> ru ~ ID

5'-

('t:r.o ,

ID ~ il> H .....

CI)

'+-! o il>

S ...... E-c c: o ...... ...., rd 0.0 CIl 0., o H il!

2

/. -0

{l0

. cg~

" 0

1 - , ti 10 15 20 25 30

Distance frorn Explosion Point (mm)

Figure 9(a). Propagation Time vs Distance :from Explosion Point for Pentolite-Quartzite Coupling.

,.j::.. .....

-(J

Cl) CI)

'-g Cl) ;::­ru ~

CI)

CI)

Cl)

k .;...J

U1 'H o >-

.;...J or! (J

o .-!

Cl)

:> s::

x 10

800

700 o

600 A ___ ).,.8

o

500 ~v

09 400 .;...J

ru ~ ru p. o H

Çl.;

j l , , 1 , t 300 . 5 10 15 20 25 30

Distance !rom. Explosion Point (mm)

Figure 9{b}. Propagation Velocity vs Distance from. Explosion Point for Pentolite -Quartzite Coupling.

~ N

CJ ~ CIl 1 :i.

~ :> CIl ;:;

CIl CIl ~ l-t

.;...> U)

'H 0

~

8 .r-< E-;

~ 0

.r-< .;...>

Cil en CIl 0.. 0 l-t

D.i

51

(;,.-

3~-

21-

1

/'

1· __1 ao 25" :SO 40

Distance from Explosion Point (mm)

Figure 10(a). Propagation Time vs Distance hom Explosion Point for Pentolite - Magnetite Coupling.

.r.>-VJ

u C> UJ

...........

S -C> :> CIl ;s:

UJ UJ C> H ...,

CI)

"H a >. ...,

• .-1 U 0

r-I C>

:> R a

• .-1 ..., CIl tO CIl P-. a H Il!

xlO 800

700

600

500

1

400

'-300' 5 10 15 20 25 30

Distance from ExpIas ion Point (mm)

Figure 10(b). Propagation Velocity vs Distance from. Explosion Point for Pentolite-Magnetite Coupling.

~ ~

C\J

E -u '-0' "

r·' 0

X

Cf)

Cf)

w 0::: 1-Cf)

250'-

200

150'

0

100L 0 ./ 0

0

0

/ 0

0

0

501- /0 0 00

0

J----------L- <_-_,_ 10

CO i/, PRE S S 1 BIll T Y

0

0

'-20 --_._------~--

yo- y

Vo

Figure 11. Com_pres s ibility vs Stres s for Quartzite <

-,-__ -.-L __ 30

_2 X 10

~ U1

- 46 -

Further, the behaviour of the shock propagation velocity

in the present test materials (quartzite and magnetite) is compared with its

behaviour in marble (Q = 10,000 psi and p = 2.7 g/cm3

), which was also u

coupled with a high velocity explosive (Sukrani dynamite). It is noticed that

the increase in shock propagation velocity lasts for a longer distance (~30 mm)

in marble as compared to quartzite and magnetite (~ 10 rnrn). From this con-

trast in the behaviour of shock propagation velocity in very strong quartzite

and rnagnetite (Q > 25,000 psi) and strong marble (Q > 5,000 psi) it seems u u

that in mate rials which exhibit unusually high compressibility at low stres s

levels (::::::! 80 k-bars in case of ma.rbIe) this increase in shock propagation

velocity lasts for a larger distance irom the explos ion point. With the same

reasoning, one can explain that due to relatively very low compressibility of

the rnetals at these stress levels (stresses irom conventional explosives),

this rise in 'shock propagation velocity has never been noticed in metals.

Lastly a comparison of the attenuation in the shock propagation

, velocity against distance shows that it is the highest in case of marble (18),

intermediate in case c;>f quartzite and magnetite and lowest in case of metals (21)

(steel).

Comparison of the Theoretical Seismic Propagation Velocity with the Measured Shock Propagation Velo city

The theoretical seismic propagation velocity for these rocks

computed irom Eq. (9) are as follows:

quartzite:

magnetite:

- 47 -

E (1 -v) p(1+v)(1-2'v)

12.24x 106

x 70.3(1-0.085) = 2.62(1+0.085)(1-2x 0.085)

= 5700 mis

(From Table 3: E = 12.24 x 104

psi,

v = 0.08'5, P = 2.62 g/cm3

and 70.3 is

a conversion factor to convert lb/inz to

g/cmz ).

E (1 -v) p(1+v)(1-2v)

_ [;0.16 x 106

x 70.3 (1- 0.284) -~f. 38 (1 + O. 284)( 1 - 0.284)

= 5200 mis

(From Table 3: E = 10.16 x 106

psi, 3

v= 0.284, P = 3.38 g/cm ).

Referring to the propagation velo city vs distance curve (Figure 9(b»,

there seems to exist for quartzite two points (A, B - measured propagation

velocities) corresponding to the theoretically calculated seismic velo city of

5700 rn/s. But due ta significant changes in E, v and p at high pressures, ,

the theoretically calculated seismic velocity from static elastic constants at

the high pressure corresponding to point A is uncertain. Hence, the most

probable zOP.e corresponding to t1.e theoretically calculated seismic velocity

is beyond point B.

- 48 -

Taking the calculated seismic velocity as reference, the

various zones in the propagation velocity vs distance curve are defined.

A low velocity narrow zone exists near the explosive-rock interface and

the measured propagation velocity in this zone is lower than the sonie

velocity. Next to the low veloeity zone is the maximum propagation

velocity zone, whieh is followed by an intermediate velocity seismie zone.

The difference in nurnerieal values of the theoretically cal­

culated seismic velo city (5700 mis) and the direetly measured propagation

velocity in the seismic zone could be attributed to non-homogeneity of the

rock substance, deviation of the properties of the rock substance from a

perfectly elastic solid and the variation of elastic constants with pressure.

The above discus sion also applies to magnetite.

- 49-

TABLE 1

Magnetite:Pentolite Pin-Contact Plate Experimen~~~

Specünen Plate Rock Shock Shock MaximUln Maximum Stre s s

No. Thickness Density Propagation Propagation Particle (kg/Cm,2 )

(mm) (g/cm3 ) Time Velocity Velocity

(/-l.-sec) (m/sec) (m/sec)

1 6.35 3.77 1.411 5070 1345 25.70 x 104

2 6.35 3.52 920 4

1. 307 5070 16.41 :x 10

6.47 3.61 1. 282 4

3 5100 1493 27.50:xl0

4 6.60 3.65 1.423 5120 1279 23.90 x 104

5 6.65 5130 869 4

3.72 1. 380 16.58 :x 10

6 1

6.76 1. 296 5200 1152 4

3.58 21. 45 :x 10

1

6.96 5230 1020 19.80 x 104

7 3.72 1.429

12. 19 2.174 6200 744 4

1 8 3.93 18. 12 x 10 - 4

9 12.54 3.65 2.293 6000 802 17.56:x 10 1 1

t 4 1

10 12.62 3.63 2.266 5980 760 16.49x10

11 5920 4

12.70 3.57 2.140 918 19.40 x 10

12.75 3.61 763 4

12 2.217 5910 16.28xl0

13 3.47 2.360 5850 669 4

13.03 13.58 x 10

13.46 3.69 5720 4

14 2.449 597 12.60 x 10

15 18.79 3.61 3.282 5460 525 4

10. 35 x 10

16 19. 10 3.50 3.459 5460 479 9. 15 x 10 4

17 19. 17 3.53 3.418 5460 4

737 14. 20 x 10

18 19.30 3.48 3.469 5460 522 9.91 x 10 4

19 19.55 3.52 3.507 5460 656 12.60 x 10 4

(Continued)

1 ;

- 50 -

TABLE 1 (Continued)

Specllnen No.

20

21

22

23

24

25

26

Plate Rock Shock Shock Thiclmess Density Propagation Propagation

(nun) (g/CIn3) Time Velocity (fJ.- sec) (In/sec)

25.24 3.70 4.675 5460

25.32 3.90 4.489 5460

25.40 3.75 4.579 5460

25.42 3.74 4.374 5460

25.47 3.60 4.630 5460

25.52 3.93 4.708 5460

29.48 3.60 5.338 5460

Average Density = 3065 (g/ CIn3

)

Standard Deviation = 0.04(g/crn3

)

MaXllnUlU MaxiInUfil Stres s Particle (kg/ CInz ) Velocity (rn/sec)

256 5. 17 x 10 4

276 5.88 x 10 4

339 6.94 x 10 4

il. 423 8.64x 10·~

391 7.68 x 10 4

288 6. 18 x 10 4

388 7.67x10 4

(

Specimen No.

1

2

3

4

5

6

"1

8

9

10

11

12

13

14

15

16

17

18

19

20

- 51 -

TABLE 2

Quartzite-Pentolite Pin-Contact Plate Experiment Data

Plate Rock Shock Shock

Thickness Density Propagation Propagation

(mm) (g/cm3) Time Velocity (fJ.- s ec) (ml aec)

6.00 2.66 1. 200 4800

6.29 2.62 1.344 4860-

6.35 2.68 1. 260 4900

6.40 2.66 1.446 4920

6.42 2.66 1. 365 4930

6.57 2.59 1. 503 5000

11. 58 2.68 1. 899 7400

12.80 2.65 2.069 6700

12.80 2.64 2.221 6700

13.51 2.65 2.421 6430

13.61 2.66 2.379 64-00

19.05 2.66 3.404 5350

19.43 2.68 3.626 5350

19.45 2.68 3.514 5350

19.81 2.65 3.300 5350

20.39 2.66 3.499 5350

23.16 2.67 4.048 5350 .-

23.21 2.70 4.039 5350

24.99 2.66 4.224 5350

25.45 2.67 4.510 \ 5350

Average Density = 2. 65 (g/crn3

) 3

Standal'd Deviation = O. 02 (g/crn }

MaximUlu Particle Velocity (m/sec)

1221

1276

1036

1065

828

794

480

484

731

647

714

437

548

:)30

376

346

499

347

269

306

Maximum St:t:ess (kg/cm

z )

15.59 x 104 . 16.25x 10

4

13.60x 10 4

4 13.94xl0.

10.86 x 10 4

10.28 x 10 4

9.52 x 10 4

8.59x 10 4

4 , 12.93 x 10 ' 4

11. 02 x 10

12.t6xl0 4

6.22 x 10 4

7.86x10 4

4.73 x 10 4

5.33 x 10 4

4.92 x 10 4

7. 13 x 10 4

5.01 x 10 4

3.83 x 10 4

4.37x10 4

,( '.-

- 52 -

Maximum Particle Velocity

The nlaXllnUm particle velocity versus distance curve

(Figures 12 and 13, semi-Iog plot) shows that for both magnctite and quartzite,

the maximUlu particle velocity attenuates continuously with distance but the

attenuation in the vicinity OI the explosion is higher as compared to its

attenuation away from it.

The attenuation in the maximum partic1e velocity_against

distance can be expressed by the equation V = V jx (where x is distance, x x e

o f is attenuation constant and V is maximum par ticle velocity ô.~ any distance

x

x). The numerical values of attenuation constant (f) for these test materials

are as follows:

Peak Stress

magnetite: 0.07346 ( Je. < 12.75 mm)

0.03779 (12.45 mm < x < 29.48 lum)

qua.rtzite: 0.07952 ( x < 12.86 mm)

0.05283 (12.86 n'nu < x < 21. 66)

The peak stress (Figure 14, ,/semi-Iog plot) was computed

- x from Eq. (6) and plotted against scaled distance z (::: cl' whe:;:e x i.5 the

distance from explosion point and d is the charge diameter). This curve

shows that the peak stress attenuation (against scale'ct distance) in the stress

wave ab ove 160 le-bars for magnetite and above 110 k-bars for quartzite is

lower than its attenuation below these stress levels. The lower peak stres::;

attenuation (against scaled distance) above a certain stress level can be used

as a guiding factor for the choice of the explos ive for the se rocks. For

example, the explosive transmitting considcrably above 160 le-bars pressure

(

" ,., ~

", ,~

(11

"

o o

o

o o

100'-" ----

- 53 -

o 0

o

" 0 0 0

0

0 0 0

0

0

0

10 30

Distance Îrom. Explosion Point (rnrn)

Figur8 12. lvlaxim.um. Partiele Vclocity vs Distance fOl' Pcntolite­Quarbite Coupling.

(

U Q)

rI;

20001-

1 1

j , o o o

o

- S4 -

............. 10001- o

o c

r' ç:: ~

"' ... ·w 'n lJ 0

.-j

Q)

'--,--~ ~.

U ·~I .J

C-I ,-'

... , C"

~ . • ,-j

~~! r0

I.",:-i

k

1

\ 500;-1

! , ,

1 200~'-

~

\ , 100\:....1 -------',

10

o o

o 0 o o

o

o

• ., 1)

o

o

,------~I----------_!I-________ ~ ________ ___ 20 30 40

Distance [rom Explosion Point (m.rn)

Figure 13. MaxirnUlYl Particle Velocity vs Distance fOl' Pcntolite­Magnetite Coupling.

(

- 55 -

in magnetite (a.bove 110 k-bars in quartzite) n'lay result in lower powder

factor (= lb of explosive/ton of rock crushed) by crushing it over large

distances from the explosion point.

The attenuation in the peak stress against scaled distance can

be expressed by the following equation (J = (J _az (where z is the scaled z zoe

distance and a is the attenuation constant, (J is the peak stress at anv z .

scaled distance z). The numerical values of attenuation constant (a) for

these test mate rials are as follows:

magnetite = 1. 121 (> 160 k-bars)

-. 2.836 (160 k-bars > S > 60 k-bars) x

quartzite = 1. 012 (> UO k-bars)

= 3.281 (110 k-bars > S > 50) x

The expected Jnaxilnurn possible error (for 1/4 in. quartzite plates)

which can be introduced in the sh"es s Illeasurelnents is estiIllated here.

Percentage Possible Errol'

FrOIll Eq. (6) we have

(J = pC v L

St;-" ss = density x stress propagation velocity x particle velocity

=

=

=

Illas s x

voluIlle plate thicknes s

tiIlle t 1 surface velocity

x 2

Illas s plate thicknes s x x

gap distance l

~~tl~'l-n-e--t--' x 2 area x plate thicknes s tilne t 1 2

Illas s 1 x

~ (diaIlleter of the plate)2. tiIlle t 1

gap distance .', 1 Je. -'î.. 2

trIlle t2

- 56 -

"

mass 1 gap d:i.stance ;:: 0.6-1 (diameter of the plate)i.! x time t

1 x time t

2

0.64 M 1 G

;:: -z x x-D t

1 t2

0.64 -2 -1 -1 a - MGD t

1 t Eq. (a) 2

From this equation we find that a is a function of M, G~ D" t 1 and t2 ~ndepen-

dent variables. Let oa, oM, oG, oD, ot 1 and ot2

be the small increrncnts

(0·,- crro~:sj in the variables a, lVi, G, D~ t1

and t2

; then by partial differ-

cntiation:

)

oa ;::(-~) oM -1- (-~ ~, oG +(~_~) aD 'I/~a)ot +( ~)ot . dM oG J \OD / \êJt 1 l \ü t

2 ?.

Eq. (b)

or

-2 ~i -1 -3 -1 -1 oa ;:: (0.64GD t1

t2

) ôM -1- (-ZD x O. 6-1MGt1. tz ) üJ) +

-2 -2 - 1 -2 -2 - i (-Hl x O. 64:1vlGD t 2 ) ôt 1 -1- (-1tz x O. 64MGD L.. )

x ôt2

(QG is very small) Eq. (c)

v"he:cc M= 269~O.1(OM)g

G ;:: O. OZO ~ 0.0003 (6G) inches

.'-b !.. O. 001 (OD) inches D -=

.,-t

1 ;:: 1. 34 : 0" 013 (ott) microseconds

·[;2 ;:: .'-

0 0 2 !.. Ov 013 (ôtZ) n"licroscconds

- 57 -

o Substituting these values in Eq. (c) we get

)

ÔfJ = 0.64{(j~~O " 3~ " 1.134 "o~z) 0.1+ o.oo{z x 2":6' x 269

x 1~~0 x 1.~4 x O~i) + (-1 x 1.;4 x 269 x 1~~O x 316 x o~z)

\

1 20 1 1) ? V X O. 2~ x 269 x 1000 x 36 x 1. 34 O. DL J

'1 r ( -2 :::: 0.0-1 i. '\2 x 10 x 2. 78 x

ç .•

,-2 -1 ) -1 10 x10 x7.45x5 xlxlO .:-

f -2 -3 2-2 \1x10 x2x10 x3.85x2.69x10 x2x10 x '0- i. 7 ,f"

1 x. '.I:!:J

}~ ( - 1 2' -2 . -2 x 5 -:- 5.55 x 10 x 2.69 x 10 x 2 x 10 x 2.78 x 10 x 5 x i.:3

-2) ( + 1 2 -2 -2 x1-O + 2.5x10 x2.69x1O xZxl0 x2.78x10 x 7."15

-1 1 -z)J x 10 x 1.3 x 10

-4 _A -4 -4 :::: 0.64(Z.08xl0 +1.5.40x10 ~+54.0xl0 +36Zxl0 )

_A :::: O. 64 (433~ 48 x 10 ~)

_A :::: 278 Je 10 ~

:::: 0.0278

Therc~:o:::e 00' :::: 0.0278

Also O' from substituting the values in Eq. (a):

Ci :::: 0.64 Je 269 36 Je 1. 34

:::: 0.357

20 1 x 100 je O.Z

:. Percentage pOG sible 01':;"01'

(~, J '

)

)

- 58 -

Method of Evaluation of the Variables and Their En'ors

M: The mass (269 g) of the plate was measured with a weighing

balance having the smallest division Tcprcsenting 0_ 1 g. The maximum error

which may occur in thi8 measurement is O. 1 g in 269 g. Thereforc l'vI = 269

and ôM :: O. 1 g.

G: The gap distance between the first two pins (Figure 4) in

the reeion of maximum surface velocity was 0.018 in. and it was adjusted

(i:'l. the shooting assembly, Figure 3) with a 0 .. 0001 in. dial-gaugc. There-

fore an 8r1'or of 0.0001 in n may OCCLU. Also to dete l'mine the maximum

surface vclocitY:1 the gap distance was plottcd against time" (Figure li:) on a

graph papar (20 x 20 to an inch) 50 that 10 divisions correspond ta 0.002.

In this ploti.;in~ a :cna.xÏ1num or:;:01" of 1 sma~l division n'1ay OCCUl"u Th>ê;J::cfore

2 1 ::hc c:"':'o1' in 1000 in. measurcmcnt D1ay be 10 x

2 1000 -

2

-total G :: 0.018 -;- 0.002 :: 0.020 in •. anù total OG = 0.0001 + 0.0002 :: 0.0003 i.n.

D: In 'che plate a maximum differcncc of 0.001 in. may occur in

the diéU:,,:;ter (6 in.) from point to point along the thickness (of the pLtte}.

'l'hercfc .;; in this case D :: 6 in. and oD :: 0.001 in •

.!2: Erxor in yeading an osciJ.logram:' The time betwecn the

two time GlaTIes 1'epresents (Figure 8) Op 5 f-I.-sec. The distance betwcen the

two time marIes is equal to 24 divisions on the steel 1'ule {64 divisions to 2i1.

inch}. The maximum error of one division may occur in the l'eading; v::lÎch

, fO.S -cOTresponus to an error 0 24 p,-sec in O. ~ p.-scc. But the actual ti~TJc" ::2:

::0 h'avcl 0.018 in. (gap distance) is 0.2 f-I.-sec, thcrefore j the Cl'l'Ol' clue tG

:: 120 f-I.-scc.

.---,

- 59 -

1 Further, an error of 200 jJ.-sec from plotting the gap distance

versus time (Figure 4) may also occur in time t2

• In this plotting 20 divisions

correspond to O. 1 ~l-sec" therefore one division will correspond to 'L~O jJ.-sec

and this is the maximum error which may cccur in this case. Bence total

1 1 ::: 120 -} 200 ::: o. 0 1~ jJ.-sec and t 2 ::: 0.2 jJ.-sec •

..!1: Following the Flame reasoning as for t2

, we get

ôt1

::: 0.013 jJ. .. sec

and t1

::: 1. 34 ~t-sec (for 1/4 in. thick plat(~·;).

Coupling Relations

By 8xtrapolating peak stress versus distance curvef; (.Fi.gt::.n!G

15 and 16) tc zero distancc$ the transmittcd pressures to the :;,'oclcs (juat at

) '~he interface: of the explosive and the l'oele) are ostimateà. The pres sure is

)

245 k-bal's

theoretical

in cas e of magnetite p

l ' f t coup mg actor p d

and 160 le-bars in case of qual'tzite v ~.l."l:.,-,

::: ratio of the transmittcd ~0 ·detonatior.

prad.JUl'e for those combinations (magnetite-pcntolite and quz,,:!.'-;;zite-pc1l.i;oHte)

can be .culated from Eq. (1).

magnetite -pentolite:

P" L :::

:::

:::

:::

2 x 5000 x 3.65 7500 x i .. 65 .;. 5000 x 3.6-5'

1. 23

P t 245

1."""23 ::: 1-:-23 - 200 k-:);, :':;.

- 60 -

l'l '

S 300;-u 0

........... () co ________ ..!.:: 200- .~~ 0

M . 0 o <")

o ~o ~ ...-i -..-. ___ ____ x

-...... .. ~---

~ 100-<!) ri ,-,

(l)

50-~

i , ~ h ~ i

----

15L._-t-__ --L-___ --!l-9 0·2.

Scaled Distance () d

(d = charge diarneter)

0·6

Figure 14. Peak Stress vs Scaled Distance.

O.ll .1.0

N

S (J , b1l ~

('1')

0 -.-,

Ji UJ UJ C)

H ;....> (/)

~ ru Cl)

!li

- 61 -

,300

200,-

100 -J 1

50'-

1

1

20~-

i 10 20 30

Distance frOIn Explosion Point (nun)

Figure 15. Peak Stress vs Distance for Pentolite-Quartzite Coupling.

50

- 62 -

o

o

50-

1

1

o

• 20f-~ _____ ~: __________ ~ ________ -L __________ ~ ________ _

10 20 30

Distance frorn Explosion Point (:m:m)

Figure 16. Peak Stress vs Distance for Pentolite-M2;::;netite Coupling.

)

- 63 -

quartzite -pentolite:

=

=

=

2 x 4700 x 2,65

7500 x 1.65 + 4700 x 2.65

1.000

Pt

1.000 = 160

1. 000 = 160 k-bars.

Now to examine the applicability of acoustic coupling, the

dctonation pressures (Pd = 200, 160 k-bars) obtained from·.the present

experiment may be compared with the dctonation pres sures repo:i."ced by

others (8, 3).

Based on Eq. (3)" a detonation pressure of 220 k-bars (fo:1.'

~ocntolite) has been obtained (8). But this pressure has been calculated on

the basis of ideal ,,-.:tonation velo city (7730 mis) which is highe2' th~n the

dctonation velocity (7500 mis) (Figure 6) measured in thes e cxpel"iments.

If the detonation pressure is evaluated on the basis oi 7500 luis (in the sam-2

equation) it cornes out t~- be 200 le-bars;) which is close to that obtained

from magnetite-pentolite expcriments using acoustic coupling ..

Another estimate of the detonation pressure for con'lparison

purposes can be obtained from the equation:

'p = cl (y + 1} P

e 1.' __ -. D

ciD dp

e

(whcre Pd is the detonation pressure, D is the detonation veloci.;y, Pe is the

explosive density and y = 1. 2 for most of the explosives).

- 64 -

Equation 11 can also be written as

0.45 n 2 p p ~ ----:_--=-~-e

d 1+0.8p e

(0.45)(7500)2. (1. 65) ~ 1+0.8:x:L65

~ 180 k-bars.

(Substituting the values of n and p ).

e

The cOlnparison of the detonation pressures from the acoustic

coupling with the two methods (which are liable to have more than ~ 10 per

cent variation in detonation pressures) indicates that acoustic couplil1g is not

rnuch more inaccurate, and estünates can, therefore, be luade using this

simple theory for the transfer of explosive energy to the rock.

Compressibility

To investigate the response of the rocks to shock further,

the compressibilities of these rocks at these high pressures were also cal-

culated. The calcu::'ations (7) were made frOlu the following set of equations~

s s o

Eq. (12)

Eq. (13)

where Sand S are the stresses behind and in fron:: of the stress front res­o

pectively, V and V are the cor responding specific volumes and v is the o

particle velocity behind the front.

(

- 65 -

Peale stress versus compres sibility curves (Figures 11 and

17) for these rocks show that quartzite becomes highly compres sible above

120 le-bars, and magnetite is likewise above 160 le-bars.

cJ

8 u

........... co ~

(t)

o ..-<

~ [J)

[J)

il)

H -i-' Cl)

o

('-~-~ 25CJ

j-

, /-200;-

1 , 1

150,­i t 1

1 !

100;--

o 0/

o

o 0/ 00

G /'.)

// //~

o

1 ( / 'j

('/ /"

< /

. C / "0' ('.-' - .-" "

1 t i

i r , /

01/ i,1

(V -v\

Comprcssi1; i1 it.y _0_ , V

(.

Figure 17. Cornpressibility vs Stress for Magnetite.

!

::>0

'1

X 10-2

C' V'

)

- 67 -

PHYSICAL PROPER TrES OF THE TEST ROCKS

Purpose

The purpose of determining the physieaJ. !HOpcrtics of the

l'oeles eonee rned

velocity (CL "

lS to elas sify the rocles and ta eompnte the prCiy.lga!:ion

p (1 ~ ~ \ ( ; ~ 2 ,,) ) of the s eismic wave fox con-> pa.r '""~ ii with the propagation veloeity of the shock wave.

Approach

In this testing~ the classification system proposed l'y

Coates (5) has been followed. Uniaxial compressive strel1.gd1.;l contjl'aity~

banding3 Îailul'e and pre-failure cha:racteristics of the rock éne the val':!.O~lS

clements of this clas sification systelu.

Testing

One inch diarncte::.:: COTes were drillcd pe;':pcn.J~CtlJ.2.·:J :7~1C:

bandi:1.g with a powennatic laboratory drill machine in the Ga:r.c.c lum:'J.<>::Ji

:::ocks (magnetite A~ B and quartzite) fl'Olu which 6 :in. di~::ne:e:L' cores v.·(;:r~

drilleâ. for s:":'cing the :rock discs for the pin-contact plate expe:r.in1cnt. :(',,~~:sc

cores were t11en reduced with a wate:- cooled clialuond saw to approxün2.;:e:\.~r

halI-inch length for Brazilian and 2 in" length dl.eng~ ~ 2 ) for unia~..::~d . ( " . _. lameter 1

compression testing (16). To reduce the dinîensional diffcrcnce :.noJt:.:

length and dianlCi;cr to the desi:red tolerance (less ihan Oy 00 J. in~; (':::.>:

point to point on the specimen,'? the specimens wcre lu· .... , ;:!:t. ::,idE! an;", (-:1",

- 68 -

<~ mctrically opposcd wirc resistance strain gauges. For Pois son 1 s ratio r ....... "

,;

determination, the specimens were specially gauged with ras ette gauges. The

specimens were then tested in a Tinius Olsen (300, 000 lb) hydraulic tcsting

machine La which a Moseley autograph X- y recorder was coupled fo:' plotting

\ ui strcs s -strain curves. A typical stres s versus strain diagram for thesc

rocks has been shawn in Figure 18. The data obtained from fuis testing has

bccn prcscnted in dctai! in the Appendix and a brief summary of the results

is as follows:

TABLE 3

Physical Propertics of the Rocks

!- Magnetite Ma.gnetite 1

Propcrty' Quartzite ~ _________ -{ ______ -;-__ ~ _____ A_--= __ ~ ___ B ____ -,

Young' s nlOc1ulus (E)x psi

Uniaxial compre-· a sivc stre;1gth (Q ) psi

u

Uniaxial telLS ile stren[;th (T}XXX psi

; ::..Jcnsity ( ,

6 6 6 1 12.24xiO 11.25xl0 9.07x:"C 1

( C. V . xx = 5. 1 %) ( C. V. = 9 . 8 %) (C. V. = 1 '1.0 %)

35,029 (C. V. = 15.4%)

1,273 (~. V. = 19. 6 %)

2.62

0.085

33,328 (C. V. = 24.5%)

1, 3[; 7

(c. V. = 19.7%)

3.37

O. 188

24,657 (C. V. = 21. 7%)

800 (C.V. = 24.5%)

3.39

0.38 i

XE was determinecl at 50% Q (secant modulus) from the finalloading u

cycle when l'lw specir,ücn was loaded ta failure. )''"

\"J\.. Cu V" == Coefficient of val·iation o

T = /'0 ~-

1rtd (B:i.'é1zilian testing).

- 69 -

Prc-Fai~L:"C Characteristics

The time dcpcndcnt flow exhibited by thcse test :·jpecimens

at a constant stl"ess of 50 pel' cent Q was plotted as log t versus defo:rmation u

and then extrapolating these deforrnations to 200 minute 8 1 the following values

of strain rate were obtained:

quartzite = 0.00 micro in. lin. /hr

magnetite A = 0.60 micro in. lin. /111'

magnetite B = i.7 micro in. lin. /h1'

Failure Chal"acteristics

The penuanent stl"ain experiencec1 by 1:hes c tCtit l"ock~ al.:

zc::.'o stress aHer each cycle L'om 25. 50 and 75 pel' cmt Q was;::ê.lCC1: ,!~" a. u

H1C:LSllTC of the plastic stl'ain. These value::; of pcrnlanent seraiL. '.'icrc

2..gainst the con:esponding pel' c<:;:rü Q Irü:lî whic:l it V:;L~: ~)~'();;F!:: U

te L;Cl'O and thcn by extrapolaLing this CUTve -Co 100 PC}" cC'n;; Î) ., h'!~: ii:'."-'~ '.

oI the pc:rmancnt strain ai; failul"e \Vas obtained. The pe:;:nlancïlL ~; o:"·"\V:.-

100 pel' cent Q a:re as follows: U

quartzite = a pel' cent:

luagnetite A = 9. '7 ocr cent

rnagneE::c B = 9. 7 pel' cent

From the various static rnechanical prop~!).·!:i;;:, ., ... .,I,y ... ___

,.~c 3 and with sorne addition2.1 inlornlation both n',l3::'c:-:"~·~;

(Q > 25:; 000 Dsi), clastic '(strain r;-,:c less thall. 2 nlic:co .iJ~I=;) .;J, .... ,\t .• , 'Ll -

)

)

- 70 -

and b:rittle (less than 25 pel' cent of the total strain before failure being p{;r-

mancnt). Field observations of the rock mass (for both magnetite and quartzite)

indicate that both the :wcks can be classified as laye:red and solid {joint spacing

greate .... than 6 ieet (!.:.::.

In addition to this classification the test data indicates that

the:ce ~" a tendency c: an increase in the value of Young' s modulus (from

9.07 :x: 106

to 11.25 x 106 psi)~ uniaxial compressive strength (from 24,637

'to 33~328 psi) and a decrease in density (irom 3.39 to 3.37) with the increase

in silica content in 111agnetite. The stress-stl'ain curve (Figure 18) for a11

thesc test rocks appear to be linear over a large portion of the:i.r ran~:c.

(

· ,

.-..",

~ )

30000 i-

25000 ! :f" '1 ~ "

tl

20000 -

QUARTZITE' SPECIMEN

Ai' li ~

- 71 -

MAGNETlTE

ûlAGRAM SHOWING THE MODE OF FA/lUF?E OF aUAFH Z '1·~ AND MAGNETJTE

~ 15000 if

(/)

Q,

(j) (j)

t'J C" .~

~; 10000 ..

.'(

1

1

5000 -

/

-.r-.I',,-.~ - - .::_ -----0' '._ ... _~_ .. ~-~~ .... _ .. _~ ..... o 500

./ ./ ./ ./

./ ./ ,/ ./

----.:,... S'mAiN - IVllCRO irvJîI

1',1 f\ G N'ëTiTE VARIC:TY "8"

Figure i8. Typical Stl"C~;s-Si:c';-cin Diag:rarn or the Vari.ous Bocks Te,.;tcÜ.

)

)

- 72 -

CONCL USIONS

Acoustic coupling theory, secms to giv\: a fair approxi-

mation ta estimate the transfer of the explosive cnergy for these rocks

(magnetite, quartzite).

2. The shock wavc propagation velocity incrca~; ,::s with

6.~.:; ~él.nce during the first 10 mm of its tl"avel fI"om the rock/explosive

(pentolite) interface for these rocks. This behaviour of shock propagation

vclocity in rocks (magnetite, qual"tzite) is contrary to its behaviou:t in mctals

(L: .!.nd is prcsumably due to high compressibility of thcse rocks in the vicinity

3. In the magnctite and quartzite both maximum particle

velocity and peak stress close-in (max. ~ 25 mm)' to the explosion point

attenu,'..l:cs exponentially. The dccay in maximum particle velocity lS more

Pl"c,.ounccd at high stress levels~ while the attenuation in peal\. stress is

grcatc r at J.OW(! 1" s'cress levels. The distance attcnuation coefficients for Làe

peak s'Cress (computed from instantaneous shock propagation velocities) werc

:found to ";:,~

magnetite:

quartzite~

1. 121 (o' > 160 le-bars) z

2.836 (160 le-bars> (J > 60 k-bars) z

1.012 (o' > 110k-bars) z

0.3281(110 le-bars> (J > 50 le-bars). z

/ ( ...

- 73 -

The reported (7) distance attenuation coefficients fOT the peak stress (com.puted .

from mean shocle propagation velocities) are:

magnetite: 0.8 (a > 150 le-bars) z

1. 4 (150 le-bars> a > 30 k·.bars). z

4. Quartzite above 110 le-bars and magnetite above 12.0 k-bars

_._~·essure become highly compressible.

.~'}

- 74 -

.' '\ t J REFERENCES

)

1. Austin, C. F., Cosner, L. N. and Pringle, J. K., "Shock Wave Attenuation in Elastic and Inelastic Rock Media", Research Department, U. S. Naval Ordinance Test Station, China Lake, California (1965).

2. Bauer, A. J "Application of Livingston Theory", Canadian 1.1.dustries Ltd., Montreal, Canada (1961).

3. Brown, F. W. li "Determination of Basic Perfol'mance Properties .of Blasting Explosives", Vol. 5i, No. 3, Quarterly of \:he Colorado School of Mines (July 1956).

4. C1~"_'les, J. 1-1., "Coupling Between Unconfined Cylin.drical Explosive Charges and Rock", I\.1ining Research Laboratory, Colorado School of Mines (1963).

5. Coates, D.F., "Classification of Rock Mechanics", International Journal of Rocle Mechanics and Mining Science (May 1964),

o .. Coates, D. F., "P:cogl'ess Repol·t 1965 Blasting Rcsearch"~ FMP 65/131-MRL, Mines Branch, Ottawa (1965).

7. Sz-..s sa, E. and Coatcs, D. F. J "Stres s Waves Close-In from Surface Explosions"~ FMP 64/126-MRL, Mines Branch, Ottawa (1964).

8. Coole, M.A., "The Science of High Explosives", Reinhold Publishing Corporation, 35, New Yorle (1963).

9. Coole, .1\11. A., "Behaviour of Rock Dtu-ing Blasting", Interrnountam Research and Engineering Company, Inc., Salt Lake City, Utah (1965).

iD. Curran, D. R q J. AppL Phys. 34, 2677 (i 96;;_

i1. (a) Dapoigny, Jo, Kieffer~ ,~" andVodar, B., "EtudedelaConllJarison des lVlillieuT Deuses a Partir de la Radiographie d'une onde de

(bj

CIl lT' Il C'~ A d S' -:::> • 2 Lf ,- '", 1 i 95 7 ) LlOC.C nIque, .1-<'. ca. Cl., 1: arls, .;:::J, . •. ,";;~ \ •

SchaH, IL ~ "Unte:csuchungen an Detonatiosstonssellen in Leichtmctallcn zur Bcstin1YX')'\ . der Zustandsglcicbung de:c'

Mctallc". Explosivesl:offe. é,_''/58).

)

\ j

- 75 -

12. Doran, R. G. ~ "High Pressure Measurements.Symposium" p New York City (November 1962).

13. Duif, R. E. and Houstcn::! E •• "Measurement of the Chapman-Jouguet Pressure and Reaction Zone Length in a Detonating High Explosive", Jour, Chem. Phys. 23, 1268 (1955).

14. Duvall, G.E., "Some Propertics and Applications of Shock Waves", Poulter Laboratories, Stanford Res,,;.' :ch Institute, Menlo Park, California (1960).

15 .. Fowles, G.R., "Investigation of Equation of State of PO:i:ous Material"~ WL TDR 64-59, Research and Technology Divj!:jicn~ Ai::: F<;>rce Weapons Laboratory, Ai::: Force Systcms Corm.'l1<-I..l,ct: I\:i:ctland Air Fo:;:cc B2.se, New Me:dco (August 1964).

16. Gill, D.S., "Uniaxial Cornprcssion as an Element in a Classification of Rocks"~ M. Eng. Thesis~ Mc Gill Univcl·sii:y,. iVlG"lI;J:.·,~al,

Canada (August 1963).

17. iEno, K., "Shock Wave Thcol'Y of Bla::.;ting"" ,,2aa::"L:c:::J.y Colorado SchoolofMincs, Vol. 51, No. 3 (1956).

18~ I., Tcrada~ lVi. and Sakul"&i, T., "Stres f; .,·ve:; ~ln Rock:; ;_.lcl Theil' Effects on Hock B:cea~(agc"3 I\:yo-co Un:iv~:;:~;i;:y, Vo:.. XXII, Part 1. I<yoto, Japan (Janual'y 1960).

-'J. I{olsky, H. ~ "Stress Wavcs in Solids"~ New York DOVC1' Publication:; In c • (1 96 3 ) •

20. Lacianyi, B., "Uniaxial Testing 01 l<.ocks fo~r Clai>sihcation Purposcs"~ FNIP b L1/i41-MRL, Mines Branch, Ott<:.wa {196-:lj.

2:i.. N~i:ashall, F.S., "The Dynarnic Rcsponse oi Iron ane1 I1"o:~-.Anoy;; LO

Shock W .. vcs"~ Los Alamos Scicntific Laboratory oi' th(::lh:~vc:i'sity

of C,,::'i~"0:..~"üa, Los Alamos, New Mc::ico (1()6C;

22. NlcQuecn, R.G. and Marsh, S.P., J. Appl. Phys. 3i. ~?S3 (S';6CJ).

23. Pal-sons, l{. C. and Sullivan~ J. D. > "lVtocluli Dctcrn1in.li:.i,,;-: :fo·,· ELLiot Lake Stres s Relief Oyercoring Work", FMP :).r::/~ r:: ··ll/[f~_,~" .'f\::ïines Bl"anch;J Ottawa (1965).

24. Parsons, R. C., "Physicai and J\!Lechan.ica::' P:;:opc:::ti...:;.; 0;: :,J~_~"(J:' j"o'CJ lrn

Ol'C", FMP 65/104-MRL, Mines Brand::." O~L;oL'.·.'a. (1<;:':):1.

- 76 -

25. Guartcrly of the Colorado School of Mines, Vol. 55. No. 4 "On Fractures Caused by Explosives and Impacts" (October 1960). ,

26. Shrefflcr, R.G. and Deal, W.E., J. Appl. Physq Vol. 24, 44(1953).

27. Sas ~;a, K., "Stress Analys is for Crate ring", FMP 65/121-MRL, Mines Branch, Ottawa (1965).

~~3. Atchison, T. C. and Tournay, W. E., "Comparative Studics of Explosives in Granite", USBM RI 5509 (1959).

29. \Vacherle, J., "Shock Wave Compression of Quartz", University of Ca!ifo· "nia, Los Alamos Scientific Laboratory, Los Alamo~, i.\ew Mexico (September 1961).

30. Walsh, J.M. and Rice, M.H., J. Chem. Phys. 26. 815 (1957).

31. Schmidt, Av" "The Theory of Compression Impact in Gases and the Detonation Wave", Zeit fUr das Ges, Schiess-und Sp:rengstoffwesen (May 1932).

32. Cook, M. A., "An Equation of Statc fo:;.: Gases at Extrcmely I-ligh Pressures and Telnperatu:ces from the Hydrodynamic Thcory of Detonation", Jour o of Chen1. Phys. > Vol. 15~ No. 7. 518, (July 1947).

33. Jones, I-L, "The Properties of Gases at I-Iigh Pressures which can be DedL:ced !rom Explosion Experimcnts". Third Symposium on Combustion Flame and Explosion Phcnomenon. 591 (1949).

Becker, "D .L"\.. , Ztschr. f. Phys. S." 335 (1932).

35. Cole, B.R., "UnÇJ.erwater Explosions", New York .0over Publ ications. Inc. (1965).

36 v Scorah. J., J. Chem. Phys. 3~ 425 (1935).

"-.) AP P::::~DiX

t.':\'V;..XL\L COI",:LPRESSION TEST DATA

---_._._-_.~-,-.---._---:--.

Specimen ;:, Dé~ C l.::-.:-! e:--J.. _ L

~, .. ra te I"ial :N" o.

;

:::t. (;'.1... .; -. f-~... ; J. r .L ~ t r ... ) rI' 1 ~ -, 1 .( L'_nol-h, 1 D.c!.rnece1., Dens .. l.) RaL"o lb S-_CLot -, Cl , .,du_us, E,

r·-----·-·

s _ci~~--'--'--'-l P~-iss~~~i-;-r L02Z1~Y:-;;es~ >e Youngls

in. , in. 1 Ib/sq in. u lb/sq il: , -,- ----,- 1 1 -_. ---1--

'~ 2 '..la 1" tz i t ,-~ 1 2 3 4 5 6 7 8 9

1. 953 2.028 2.014 1. 95 i. 1.998 1. 953 i.799 1. 455 1.444

0.982 0.982 0.980 0.982 0.985 O. )87 0.983 0.979 0.981

2.628 2.6L.~2.

2.639 2.630 2.589 2.589 2.612 2..635 2 .. 627

Average compressive strel,-gth Coefficient of 'varial:ion Average Young' s r.noc1ulus Coefficient of vari?tion Average Pois son' s ratio

1 Average cl(;nsity I-'--'-'~-~--'-----'---l-'~----'----' ,- ~-.-

3 , :::::::: 1

\i,"'(',,,-(i~,,,, ,\ 1 1 ~ or-O 0 969 1 3 ~ ~o? .. , .. c-~_.C __ L~.,- 2 1 i~~~3 0~954 \ 3:(6:.

\ 3 1 L 8"! [3 O. 968 1,986

3~ ?.:;6 0.970 ") ~ 1 • :; . ~;' ~.;. i

i Q;;5 1 0 Q;'8 ~ "/... ~ c ~ '...J

~ (". () ;- J 0 C\ ", ? ? -, = :: .'. ',-,/.(~~ _, _-~ __ ': .. 2 ~ __ , ~ ~.(. -:~ .. : ___

l '~

_._" ~J __ , ~ __ . L

0.062 20,250 21,400 30,000 29,000

O. J.08 22,000 33,000 28,400 28,300 26,600

:: 35, 029 lb / s q in.

= 15.4:% = 12.29

= 5. 1~~ = 0.085 = 2.622

O. 123 O. 2,lD

--..... _._,-_. 1 21,00J j 1 (.6,300 1 l ')<) ~30 1 1 .... 0,- 1 1 i5,7('0

\ 21,1(10 1 3/1,550

- .. ""- .. ~ ........ _- '---",-~-",,--_ ... _.-

26,737 28,256 39,773 38,290 28,871 43, 131 37,422 37,595 35,193

2.8,476 36, 794 38,224 21,2L15 28,671 46, sr)!.

/,-;,reraGe ccu1pr2ssive stl:cn[;th = 3j, 32.8 Ib/sq in. Co':.fficient of \7él. r~2_t~.8r.l

J~'~.~ :;!"aEe '"'{(.ttllg!::: ·)v;~,.;,j.l".~~

(;~ ~(:~1(.5~.nt of v:·.:r·lC~:l.:' __ );!.

l, .... ,,:,:).' 2.f!e Pois son' s ratio ./: ./-: ~_"2..r e elen.'s it\1'"

-,.,- ," __ ~r _.-. r';r, < ,""Or---,_'" _._'. - _ ........ - ____ ~.!.:~~ _____ "'~._~_ .. ..:.... ~ _____ -______ -", ..... " ...... ,...-._..___~ __

i

= 24. SO/ - .,[. i -{i!>~ .~. 1 \J"'{} J."l}"\/'sq i" - ... ~ '...... 1. _ _l.. ... ~

= 9.8S1e.

= 0.19 = 3.38 ,----~-~---~~---~_ .. _-------~-

13.2 x 10 6

12.4 x 10 6

11.9 x 106

11. 5 x 106

12.2.8x 106

i i. 84x 1.06

1

_L9j~ 106-1

.~ __ ~J (Ccn"~"n" - -' \

J "".!..!..!.Li~ ....... _ "

-J -J

r

l I' -c::.te-('1~1 ~ . _ _ _C~.4

. ~._.=~._,.-~

1\,iê·8D.etite B

L_

\..

" .. --... ---'- '-~I .--~-----~-- . __ .-._-_ .......... _ .. -.... _._- -- ---~--_. __ ._--Spêc}Xne:n Specin1en 1 S~ecimen 1 . 1 Pois S.OE

I s 1 - _.

No. Length, Dlameter, Del-, -lty RatlO Load, 1 Compressive

lb Strength, Q ,

in.

-'-';--"I~--;-o i-; ? 2.030 3 4 5 6 7 8 9

! 2.067 2 .. JO

2.003 2.085 1. 920 1.865 1. 713

~b/sq in. u

il,800 15,968 23,800 32,273 15, 150 20,501

in. . o. 97;------'---3: 4;--r---=' ".----~::~~ ~:~~. 1 0~;20 0.97 J. 3.55 0.443 19,000 25,658 O. ;70 3.34 17,750 24,019 0.972 3.95 18,400 24, 791 0.984 3.37 25,600 33,664

19,000 25,138 15,000 19,725

0.981 3.42 0.984 .J 3.41

= 24,637 Ib/sq in.

= 21.7% Average compressive strcngth Coefficient of variation Average Young l

"" moduJ.us Coefficient of variation Avel-age Poisson's ratio

= 9.07 x 106 Ib/sq in. = 14.0% = 0.381

P,:,,-'/er2_ge den.sity" = 3.39 ------ ----~----_._-----_._--------

"--.l

Young i s 1vfodulus, E 7

Ib/sq in.

r 6.96 X 106

10.42 x 106

6 9.47x10 9.43 x 106

-J CD

• ~--. __ .- ~.:.:- -:;::::=:.. •• --=:----------._----._-_.-

" Quartzite

Magnetite A

MarYnetite B --~---

- 79 -

CREEP AND PLASTIC STRAIN DA TA

x xx E: at 25 pel' cc': Q = 0.0 pel' cen:;

p u

E: at 50 pel' cent Q p u

E: at 75 per cent Q p u

Strain rate at 50% Q u

Strain rate at 75% Q u

E: at 18 pel' cent Q l) U

E: al: 36 pel' cc: Q p li

E: at 55 pel' cent Q p li

St:i:ain rate at 50% Q u

E: at 25 Del' cent Q p U

E: at 50 ',)e1' cent Q p ...

U

E: at 75 pel' cent Q p u

Strain :rate al: 50% Q u

= 0.0 per cent

= 0.0 pel' cent

= 0.0 micro in. lin. /hr

= 12 micro Ï!1. /i:'1. /hr j,il 18t :.:n.'Ï!';"l.l:r!· and zero for the nc:;.:~ !'.!1: E, inutes.

= 1. 3 pel' cent

= IL 3 pel' cent

= 2.1 pe:c cent

= 0.6 micro in. /i'1.. Ih:.:

= L 87 pel' cent

= itl 50 peT cent

= 7. i pel' cent

= i. 7 micro in. lin. j'hi.'

X E: P

= permanent strain, calculated by t:1C formula (20) E: - 2:; E:

r v E: pel' cent -- ----:- X 1,00 P E: -~E:

total v

whel'C E: .- '2~'le total maXinl.Ul'U sl::i:ain aUahlcd ~:otal

68 V

= '::~lC total :ccsiclual sÜ'ain obsl:!.:v-::;c1 al\:~'2':

X:';:Q = CO:.:.o.DTcssivc strength of 'Ille rcspecti.vL~ ::ockv 1.1

., ~ . t.:.~~J .. 0( .. ~-=-~ ~'i~g

...

i ! 1 i "

,t

Material

~:t:..8..r·~zic0

l

Specimen No.

- 80 -

BRAZILIAN TEST DA TA

'-Th-i-c-k-n-e.,-", S-O-:-f--'I~' Diamete r of Load,' Tensilc Strengthl Specimen Specimen lb ;' '), 1

(t) ~ (d) (p) lb/ sq in. !

inches ~ inches ( '1"', 2P) , ____ -: _______ , _________ \~=_T."_t_d_'__ _ _I

1 0.984 1.370 1,620 i O. 5L1:7 2 0.545 3 0.562 .li 0.438 5 O. ~163 6 0.510 7 0.530 8 0.525

/' 0.982 800

0.985 1, 160 0.983 0.983 0.982 0.985 0.984

7"10 7.50

1,340 970

1, 110

950 1,380 1,090 • J 050 1,700 i, ~80 1,370

0.981 :/.,090 1,415

Ave:cage tcnsilc streng\:h = 0;,9:7

1

3 lb/sq ~~~ 975~1 L9 0.500

10 0.533

Coefficient of va:c"iation = ~ 9.6 pe r cent 1 0.528 1 --0-. -9-7-::'-=--'-1-,-2-'.!:-0-:--1-,-5-2-8 '

0.970 1,430 1,770 1 O. 9 '1 2 t 1, 0 8 0 i, 3 LlO ,1

2 0.530 :" O.5L1:5

0.971 820 912 O. 9·1.~ 970 1.080

\ .cJ: 0.528 1 t= 0.590 ;;1

0.973 1,300 1,790 / 0.475 0

7 O. 5L18 0.970 980 i, '. ,,0 8 0.5.l'::2 0.970 950 1, i-'lA,

9 0.470 0.971 Il,120 1,560 0.970 1,320 1,366

~~--~--~-------= i, 36 7 lbs q in. 10 0.500

[-------=---:---'-------i\.ve:.:age tens île st::::en~th

, , "

~v":":_/0·."

Coefficient of va:::iation ,

O • .cl95 J.

2 0.613 3 0.552. Lt 0.548 5 0.533 6 0.550 7 O. Li97 i

= i 9. 7 pe r~ cent

0.972 470 0.985 870 0.972 600 0.973 790 O. '~:~O 670 0.980 540 0.975 750

920. 7i.O

8:1.7

0.595 l 0.C:83 700 ~, /~--~/ --~-----'--~------

Ave:.:."age te:nsile s"t:l<en.::;th = 80-v-::l Ib/sq in. Coefficie:,: of va:datioD. = 2~L 5 per cent

" D i

"--!

C(i:':'\SRSIO:~ T.':"'~L:=S - El~I lIS::, J~·s~)I.IC:~;: /.~':D l'~l?2.C U:':I1S C.:' ,::::':.SL?jJ·SNT

] 2.._E.2..':::~ c:.r-.E

'!1~S

l r !..:

y2..:::ds ni.les (st~,l.·,·t8)

cent i!::e tre s ~>"tres

ki.lc:;;e;L

L1'icro2.s

squere inches

square reet sC[ù2.rc yards sq:.:' -:e r::iles

sq~a=e centL~etres squart oetres sçu2.re 1:il~2tres

ct!oic inches cubic fee:.t

cubic :::etres

Èto

LEEGTH

ce:1tii7:~t::-es

r:~::;.trc::s

~-~,:; t re: s ki.l C~8 tre s

ir.C!18 S feet Diles (stet.)

82trcs

ARE A

squ~re centinetres squere! feet square! cent~~etrcs square lI!~tres square l:ilc~etres

square incnes square feet square ni1es

VOL T: ,,1 E

cU~Dic centi.~.et:-~s cU):.:.c :::etr\?C'

cubic in:.be3 cubic feet

DEN S l 'I Y

Hultiolv bY:

2.54 0.30-';8 0.91!;!, 1. 6093!:-'1

0.3937 3.281 0.(,214

1 }; 10- 6

6.4516 0.00694!, 929.03 0.8361 2.590

0.1550 10.76 0.3861

16.39 0.02832

61023 35.31

P nl'~-'S/CU'Di- Iê-,' ";;o"~~"'s/cu ~c,;, .. ,o 1 r. 0' '- ...... '- __ .... ...,'- - .... .10."'- o .... ~ ,I~. __ L_,- -"' __

l:ilogrê.::'l:S 1 cu.,;.-:_ ... "-oc. pounds/ct.:bic fc' '.

Ii 1.. S S

pound (Er:81 is11) gré;;';'

8i..-L:.J pOl!.i1d

Si. e; (l~i::ëi,~ 21.) l':.:i.lO~:-<=1

pCt'I!d

O. 062!;~

453.6

2.205 x 10- 3

1L,.59

32.17

Tc c 0:;~:21' t Into

VELOCITY

inc}',::::: / sc:: c o:·~è feet/:. .. ,=-~-::~ Cfs) nilc 5 /1~ :r·-.:::

c~nti7etres/second

k ';l ~,~ ~>"o ~ /'nou~ ........... _L_t::v • ....

cent L-:!etres 1 second cent ~-:;etre s;' ",,"cend cent ~-;;etres / se.cond kilo:neters/holS::

feet/second L1i1es/hour

[ee.t/second miles/hour

ACCELERATION

inc. /seco:ld2

feG.t/ser:.o'":ld 2

centiE.etres/second2

g

cent~-;;etres/second2 g cent~-;;etres/se=ond2 ~ Q

incnes / se.c ond 2 feet/second 2

centiDetres/sec~nd2 feet/secOrlc,2

FOR C E

pcu;',ès U.:::erican)

dynes

gra-:ls

poundals

ne'h"Lons

PRESSjj

pO'.Jnès/s~'..:.-"-:: inch poun~5!S(. fo~t ,.'j ",.-/ _.,' ;~-t- 2 .b .. l_06_c..~_ C:.:..'-.~ .. è ~e

b~::s

dynes gr 2...:."':1 S

pO'.mds. gra";ls pounds dynes dynes pounds d)rnes

E 6: STRI:SS

kilogra':lfcer.tbet:-', ? kil Of,r2:i/7:,c tre 2

pounds/sçJare i==h pounds/square fc~t dynes/centiD~t~~2 kjlogr~s/metre2

Hu1tiDly by:

2.54 30.48 44.70 1.609

0.03281 0.02237

0.9113 0.6214

2.54 0.0029 30.1,8 0.0311

0.3937 0.03281

980.6 32.17

44.482 lé 104 1:'~.6

,',8 lé 10- 6 ~.\.,2 x 10- 3 2.205 x 10- 3 980.7 13 ,826 0.03108 1 x 105

0.0703 4.882 14.22 2048 106 1. 020 ~ 104

pounds/ square i::lch 14.50 pounds/square f.: . ~'39 ----

co -