in - DTIC · subsurface fracture produced by impact in rock. 2. Reproducible and controlled...

$: in - DTIC · subsurface fracture produced by impact in rock. 2. Reproducible and controlled cracking is obtained with a wedge-shaped indentor. 3. A quantitative relatienship has been$
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HIGH ENERGY IMPACT ROCK BREAKAGE RESEARCH PROGRAM

ANNUAL REPORT MARCH 1972

REPORT TM-7204

Prepared by IngersoU-Rend Research, Inc.

P. O. Box 301 Princeton. N.J. 08540 Phone (609) 921-9103

Joel W. Hollenberg Principal Investigator

Lee W. Taros Development Engineer

Mukund D. Gangal Solid Mechanics Analyst

Sponsored by Advanced Research Projects Agency

ARPA Order No. 1579, Amend. 2 Program Code 1F10

Monitored by Bureau of Mines

Contract No. H0210045 Amount of Contract $59,944.00 Effective Date: 23 March 1971

Contract Expiration 23 March 1972

\

■«Pforfucd h,

NATIONAL TECHNICAL ION STATEMENT A j fT

DISCLAIMER NOTICE

THIS DOCUMENT IS THE BEST

QUALITY AVAILABLE.

COPY FURNISHED CONTAINED

A SIGNIFICANT NUMBER OF

PAGES WHICH DO NOT

REPRODUCE LEGIBLY.

The views and conclusions contained in this document ere those of the authors and should not be interpreted as necessarily represen- ting the official policies either expressed or implied of the Advanced Research Projects Agency or the United States Government.

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Advanc«Hl Research Projvcu Agency Washington, P.C. ?03oi

The porpotc of tnis progrann i.- to study Uu« effect of fHctorr such a^ tool shape, blc.v. anorgy, ilugl« -ovu mnltiplc loration impacts ar.f! spacing on the fragmentation of hard ror:k. The major activities within the project incliulo:

/t. Theoretical Analysig »nd 'Parameter Study B. Fracture Tests on liar re Granite C. Field Tests in Variûo Formations

Annual results arc reported bl .." . >£ each of these activity areas. The go;*] of the pro-r. ... j to ol.liin a bett. r understandin,? of mechan'cal rork breakage in order to provid; for a taster, more economical method ol liad«rgrottnd excavation in hard rock formations to be eventually developed,

OetaiH of niustralffTrslfr •Uli« docifnent fr,r, b« better

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TABLE OF CONTENTS

TECHNICAL REPORT SUMMARY 1

L OBJECTIVE AND SCOPE • 3

1. Analytical and Experimental Study of Subsurface Cracking 3 2. Analytical and Experimental Study of Edge Fracture 3 3. Field Tests in Various Formations 4

XL MAJOR ACCOMPLISHMENTS 5

A. Subsurface Cracking 5 1. Introduction 5 2. Semi-Empirical Model 5 3. Experimental Verification H

(a) Static Tests 11 (b) Impact Tests • 13 (c) Observations 14

4. Concluding Remarks on Subsurface Cracking 14 B. Edge Fracture 16

1. Introduction 16 2. Edge Fracture for Pointed Indentors 19 3. Parametric Relationships 20 4. Wedge-Shaped Moil 25 5* Experimental Verification 28

(a) Spherical-Tipped Pointed Moil 29 (b) Wedge-Shaped Moil 30

6. Edge Fracture Conclusions 35 7. Summary Results of the Edge Fracture Tests 33 a

C. Field Tests 37 1. Introduction and First Field Test 37 2. The Second Field Test 37 3. The Third Field Test 4. Lab Field Tests - Five Foot Granite Cube

39 40

5. Field Test Conclusions 44

III. FIELD TEST PROBLEMS 45

IV. FUTURE PLANS 46

V. REFERENCES 48

APPENDIX A; Summary of Observations - Drop Tower Tests for Edge Fracture

B: Computer Print-Out to determine averages, means, and standard deviations.

C: Non-Isotropic Behavior of Barre Granite

•af

LIST OF FIGURES

Figure « », No. PaSe No'

1 Subsurface Crack Formation 7

2 (a) Contour Lines of Equal Tensile Stress 9 (b) Decay of Tensile Stress with Radius for a

Semi-Cylindrical Crater 9

Decay of Tensile Stress with Radius for Hemispherical Crater 10

Rock Face Designation 12

Crack Length vs. Blow Energy for a 120* Wedge 15

Evans1 Equilibrium Approach for Cutting Coal 17

(a) Action of the Moil in Edgr: Fracture 18 (b) Quarter-Space Idealizatioi 18

Stress Distribution in a Q'iartei Space 21

Hatenyi's Solution for a 22 xmax 10 Energy, Volume and Edge Distance Relationships 26

11 (a) Action of Wedge-Shaped Moil 27 (b) Two-Dimensional Idealization 27

12 Rock Fracture Parameters - Pointed Tool 31

13 Volume of Rock Removed as a Function of Edge Distance 32

14 Critical Energy as a Function of Edge Distance 33

15 Specific Energy as a Function of Edge Distance 34

16 Rock Fracture Parameters for 2 in.-90* Wedge 36

17 Primary Fracture Tests - 5 ft Barre Granite Cube 42

18 Secondary Fracture Tests - 5 ft Barre Granite Cube 42

>

iv

LIST OF PUVTES

^ate Following ^_ Page No.

1 Subsurface Crack #1 - Tungsten Carbide 7/16" Spherical Indentor, Static Indentation 13




5 Subsurface Crack #5 - Tungsten Carbide 1" x 3/8". 120* Wedge Shaped Indentor Blow F .gy = 55 ft lb 13

6 Subsurface Crack #6 - Tungsten Carbide 1" x 3/8", 120* Wedge Shaped Indentor Blow Energy = 55 ft lb 13

7 Subsurface Crack #7 - Tungsten Carbide 1" x 3/8,,, 120* Wedge Shaped Indentor Blow Energy = 55 ft lb 13



10 Subsurface Crack #10 - Tungsten Carbide 1" x 3/8", 120* Wedge Shaped Indentor Blow Energy ■ 110 ft lb 13

11 Oroptower Facility 28

12 Moil and Point 28

13 1000 ft lb Impactor Moil Points 38

14 3000 and 10,000 ft lb Impactor and Tools 39

15 Field test of 10,000 ft lb Impactor in Granite Gneiss Formation near Mt. Hope, New Jersey 40

S

TECHNICAL REPORT SUMMARY

The purpose of this project is to study, by means of theoretical

analysis, laboratory experimentation, and field testing, the effect of blow

energy, tool shape, single- and multiple-location impacts and spacing on

the fragmentation of rock, in-situ and for blocks. The overall primary goal

is to obtain a better understanding oi" mechanical rock breakage which can

provide a faster, more economical mrthod of excavation, tunneling, or

large-hole drilling in hard underground rock formations, and to examine

the potential special advantages with respect to noise and dust generation

as well as remaining formation ability that this method may enjoy.

During the first meeting on the High Energy Impact Excavation

Project, the utilization of the high-energy impact tool was visualized as

occurring in a two-step procesb. Flint, one must produce large cracks

in the rock mass and then, produce jecondary fractures fragmenting the

rock into pieces. During the past ycir both of these areas were studied,

analytically and experimentally. Excellent quantitative information was

obtained which will provide b«j<c information for all future work on the proje t.

The major conclusions reached are summarized below.

1. A qualitative understanding has been reached regarding the subsurface fracture produced by impact in rock.

2. Reproducible and controlled cracking is obtained with a wedge-shaped indentor.

3. A quantitative relatienship has been established between blow energy and crack length for a wedge-shaped indentor.

4. Qualitative as well as quantitative understanding has been reached in the case of edge fracture.

5. A critical level of blow energy exists at which a piece of rock breaks out from the edge.

6. The volume of rock broken out in edge fracture is principally a function of edge disUnce and tool shape.

7, Hatenyi's analysis« seems to explain the nature of the edge fractuxe. More rock testing will be needed to prove the variation of critical blow energy as a function of rock tensile strength and tool wedge angle.

8. Low specific energies demonstrated during the edge fracture tests show promise for a tunneling system application.

* This will be explained in detail in Section II-B of this report.

I. OBJECTIVE AND SCOPE

The objective of this research program is to study the effect of factors

such as tool shape, blow energy, »ingle- and multiple-loc.iticn impacts and

spacing on the fragmentation of hard rock samples. The primary goal of this

work will be to obtain a better quantitative understanding of mechanit.xl rock

breakage which can provide a faster, more economical method of excavation,

tunneling, or drilling in hard underground rock formations.

The work is divided into three main activity areas; these are as follows:

1. Analytical and experimental study of subsurface cracking.

2. Analytical and experimental study of edge fracture (or secondary breakage).

3. Field tests in various formations.

Each of these areas will be reported upon in the following sec dons of this re-

port. The purpose of each of these activity areas is as follows.

iL.iiffJll'itfJjÜlft.^E^JT?*!***1.??^P/.Subsurface Cracking.

This work is aimed at providing a guide for the application of high-

blow energy impact tools in rock excavation. Through the mathematical

modeling of the rock impact process, utilizing existing ami modified theories,

relationships were sought between impact tool parameters such as blow en-

ergy, tool shape, etc., and rock properties, which can be used in designing

and operating impact excavation equipment for tunneling into a solid face of

hard competent rock. Of principal concern is the relationship between tool

and rock properties in terms of the size and direction of subsurface cracks which can be produced.

This work is aimed at providing a quantitative e'escription of this

process which is visualized as breaking to an edge in the rock which either

pre-exists or is created in a massive formation by fractures produced as a

result of a sufficiently high-blow energy primary impact (see above). Through

analytical investigations and laboratory testing utilizing our drop tower

facility, relationships were sought among blow energy, tool shape, edge

distance, and material removed (specific energy fracture) for Barre

granite.

3. __Field _T®8_t8.in VfcrkMf Formations.

This work was aimed at providing preliminary experience in in-situ

rock icmo.al for hard, massive formations. Through these field tests, an

appreciation of the actual problems which would be encountered usinc the

impact rock removal process during tunneling by means of this method was

gained. To date, three such trials ha-c been carried out, one in a diabase

form-.tlon near Belle Mead, N.J. and two in a granite gneisd formation

near Mt. Hope, N.J. The field testing at Belle Mead was reported upon in

the Semiannual Report. Section II-C of this report covers the testing at

the Mt. Hope quarry.

II. MAJOR ACCOMPLISHMENTS

A.__ Subsurfar• _Crackin^

I. Introduction

Cratcring phenomena related to indentation of rocks, have been

observed experimentally and studied analytically by several investigators 1* 2 3 including Fairhurst and l^acabannc , Reichmuth, Paul and Sikarskl, and

4 Sikarxki and Miller . They observed that when wruge-shaped and button-

sha;>.■(.' tools impact rock, the rock ahead of the tool is crushed, forming

a "crater, " and then, depending upon the impact energy, chips of rocks

ma/ break out at the surface. In addition, they invaribly observed that

tensile cxacks of rather large size compared to crater size were present

at tli-- bottom of the crater. However, their observations on subsurface

cracking v/cre essentially qualitative. From the start of the program on

H'gh Energy Impact Tunneling, it was recognized that this subsurface

cracking may play an important role in this overall rock fragmentation

p'-on-ss. and hence we set out to determine the quantitative relationships

involved in subsurface cracking.

Earlier workers showed that for impact velocities encountered in drilling,

the dynamic effects may be ignored. Therefore, they modeled the wedge in-

dentation nroccss by a line load on an elastic half-space and were puzzled by

finding that the stresses they calculated within the solid were everywhere com-

pressive while the cracks indicated tensile stresses. At this point, Paul and

Gangal used a more realistic model by assuming a quasi-hydrostatic loading

on the crater, and showed that around the crater, one component of the stresses

was indeed tensile with large enough magnitude to allow tensile cracking.

Recent work of Aquino at Eell Labs appears to be the first study of

the quantitative aspects of the subsurface cracking phenomena of spherical

indentors. His work was reviewed in the semiannual report on this project.

From analytical expressions, he introduced an important concept, namely

the linear relationship between contact radius of the indentor and the crack

size. This observation «ran be used with a modified interpretation to deter-

mine crack size in rock, as will be explained later.

* Superscript Numbers indicate References in Section V.

In what follows, we will report first upon a semi-empirical model

used to study the cracking phenomena, then we will present the results of our

experiments, and finally wc will state the conclusions.

2. Semi-Empirical Model

In this subsection, we will consider a semi-empirical model for an

indentor impacting a flat surface of rock. At the beginning of impact the in-

dentor and the rock surface are deformed elastically according to the Hertz

theory until the load exceeds the crushing strength of the rock. Above this

initial crushing point, the tool creates a zone of highly-pulverized rock which

we call a "crater," The powdered rock material compacted between the

crater surface and the tool is probably under a "quasi-hydroptatir" state of

compression. Depending upon the rock properties one or more surface

chips may also be formed during the process of cratering. However, this

chipping (which is important in drilling) need not concern us here. In the

following discussion we will be infereslad In investigating the effects ot the

quasi-hydrostatic loading on the crater.

Figure 1 shows schematically the tool indentation process. For a

spherical-tipped indentor, the crater will be idealized simply by a hemi-

spherical cavity under uniform pressure, bounded by a semi-infinite solid

(rock) as also shown in Fig. 1. Alternately, for a wedge-shaped tool the

crater will be idealized by a pressurized hemicylindrical crater. Although

the idealized problems look simple no analytical solutions are available in

the literature. Therefore, it was decided to use the finite element method

to solve the idealized crater problem. The solution for the hemispherical

case was obtained using a computer programs developed for the stress

stress analysis of axisymmetric solids. Solution for the hemicylindrical

crater is taken from Paul and Gangal . Since all geometric dimensions can

be scaled in terms of the crater radius, R, unit crater radius was used in

the computation. To simulate the semi-infinite nature of the rock, the

outer boundary was chosen to have a radius which was cf the order of forty

times larger than the crater radius anda stress field consistent with the

theoretical point load and lite load soultions (for details sec Ref. 5).

The crater pressure, p, is very difficult to measure, ic is a function

of overall tool shape, energy, and rock type. Let us non-dimensionalize the stresses with respect to the pressure, p. For simplicity a unit normalized

pressure was used in the finite element computation. In reality, the pressure will alwavs be areater than n . tk«

PRESSURE - P

CRATER lOEALIZ

INCIPIENT CHIP

INOEN70R

T

CHIP BOUNOAfW

SECCNDAPY RADIAL CRACK

PULVERIZED ZONE

INITIAL RADIAL CRACK

INITIAL CRACK FORMATION

FIGURE 1

8 Figure 2 shows the distribution of the tangential stress, ae, plotted as

a function of radius. The figure also shows a stress contour representation

of CJQ. The tensile strength of the rock, ot, is usually amall compared to its

compressive strength. The tensile stress at the bottom of the crater on the

othe- hand is of the order of the crater pressure which is larger than the

compressive strength of the rock. Thus one would expect a crack to form

and grow along the center line of the crater. In addition to this central crack

several smaller cracks can also be formed as shown in Ref. 5.

Figure 3 shows the distribution of the hoop strese /or the hemispherical

crater. At the bottom of the crater, the hoop stress approaches to a value of

roughly half the crater pressure. Thus one would again expect cracking to

occur. Note, however, that in this case the tensile hoop stress field is axi-

symmetric and therefore does not have a preferred direction to propagate a

crack. Thus one should expect in this case that the formation of i single

crack or multiple cracks, the directions etc. to be determuied by rock

anisotropy. inhomogeniety, and the pressure of pre-existing mirrocracks

rather than the stress field. Once initiated, these cracks may grow in the

tensile stress region to a length, say. I, which can be several times larger than crater radius,. R. Thus,

* = aR 0) where a is a constant for a given material and tool shape to be evaluated experimentally.

Aquino followed a somewhat different course. He us ad the Hertz

theory to determine an equivalent of the pressure, p. Then he used Love's

analytical solution to obtain the tensile stress (hoop) distribution. At that

point he departed from the above method and used an approximate Griffith's

approach to determine the crack size as a func -ion of Hertz contact radius.

He then derived a relationship between "crack radius" and the equivalent of

crater radius, R, which is similar to the relationship (1) above, and evaluated the constant experimentally.

From a more practical viewpoint, in a given rock the most important

relationship is between crack length and blow energy. In the literature on

craters, various investigators* report widely different relationships between

crater depth (which equals our crater radius, R) and the blow energy. Haw-

ever, one may write a general expression of the form:

* see references 1, 2, 3. '

r -• ■ s :' -.5

1 * ,

'-•w. r 1 1 f t

>. '^9 t - - -. .

^wHTOüR LINES OF uCV.^ THU- .£ bfRftSS

DECW OF TENSILE STRESS W\TW RADIUS

FOR A 5EM1-CYLINDRICAL CRATER.

10

ft

^

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> X N

Q

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11

RaEn (2)

where E = blow energy for the spherical indcntur and blow energy per unit

length for the wedge-shaped indentor, and n = an empcrical conttant.

Thus, the crack length is also related to E as shown below

t = Kj En

The constant of proportionality and the exponent, n, are determined experimentally.

3. Experimental Verification

It was recognized quite eurly in the program that quantitative measure-

ments on subsurface crac'.ing to establish all parametric relationships would

be very costly. A limited scries of experiments were therefore planned to

study the most important parameters, namely .he input energy and basic tool

shape, i.e., the spherical tool vs. tlic wedge-shaped tool.

The object of the expcriment-.l program was twofold: first, to see if

reproducible subsurface cracking could be produced in the rock, and then,

if successful, io obtain a quantitative relationship between the crack length

and the tool-rock parameters. It was decided that the first objective could

be attained by static indentation tesU while the second objective required im-

pact tests. These are described in turn below.

(a) Static Tests

For the purpose of the limited experimental program, eight 9 inch

Barre granite cubes were obtained. Two basic tool shapes were chosen, a

7/16 inch sphere and a 1 inch by 3/8 inch, 120° wedge. In an exploratory

phase of the work, a single block was indented on faces marked B, B', C,

and C in Fig. 4 with the spherical-tipped tool. Then a dye penetrant was

applied to the crater and after waiting for about half an hour, the block was

spilt open to trace subsurface dye penetration into the crack. It was found

that the dye diffused into a large hemispherical zone under the crater. This

wiped out any distinction between cracked and solid rock. This technique

was therefore proven to be inapplicable.

12

PIG 4 : KCCK FACE DESfcaNATIOM,

HOI?.: A', ß' AWD c' ARE FACES OPPOS'TE

TO FACES A , B AMD C RESPECTIVELY.

13^

Next, an X-ray radiography technique was used. Here the rocks

were first radiographed to show the initial state. Then one of the rocks was

indented and x-rayed again and compared with the initial radiognph. It was

found that cracks could not be detected with this technique either.

Finally, a rock indented with the 7/16 inch spherical tipped tool was

cut with • diamond saw through the center of the craters, parallel to face

A It was found that the large cracks starting at the crater wrre visible to

the eye. To increase the contra** a special dye penetrant, P-135 ma.de by

Trace Tech, was used. This dyo penetrant is sensitive to ultraviolet light.

After dye penetration, each crack was photographed using ultraviolet light.

Plates 1 through 4 show the photographs of the four craters and the cracks prodiced with the 7/16 inch spherical indent jr.

Plates 1 through 4 yielded thr» iollowing observations. Only in

one case (Plate 1) was a centra! ..rack observed. In two cases (Plates 2 and

3) cracks smaller in size ami propegating at different angles than that ob-

served in Plate 1 were detected. Finally there were cases such as shown in

Plate 4 where no single major crack was observed. It was therefore concluded

that with the spherical tip, the direction and size of the major crack could not

be controlled. Similar experiments with wedges shower* rather good predicU-

bility, and therefore, all impact tests using spherical tips were abandoned. (b) Impact Tests

The objective of these tests was to establish the important relation-

ship between blow energy and the crack length for a given wedge-shaped

tool. A 1 inch long, 3/8 inch wide, tungsten-carbide wedge (120 • inclined

angle) shaped bit was cemented at the tip of an impacting moil. Our drop

tower facility* was used in the experiments. The 9 inch Barre granite cubes

were secured at the bottom, and the moil was dropped on them from prede-

termined heights. Indtntotions were made on faces D, B', C, and C. The

blocks were then cut in half with a diamond saw In such a way that the cut

passed through the centers of each crater. Once again, xrace Tech P-135

* Ihe fn tOWer f~cility and it8 *—*— has been described In the Semi- annual Report. Further description of this faculty I. given liter In ^Ts

/9<

PLATE 1: Subsuriaco Crack -]

Tungsten Cnrbido 7/: 6" Sp5icric.nl Ir.der.tor

Static Indentation

PL#\T:-: j.: ö.ii.iu:-:..■_•_ C:

Turn •*■.■:: ; 7/16" Stv. :••:,.' : : •.•. - ■

fit

PLATE 3: Suhüur^ce Crack #3

Tungsten Carbide 7/16" Spherical Indcntor

Static Indentation

PLATE 4: Subsurrac<3 Crack «4 Tangsten Carbide

i/\h" Iphcrical Indcntor Static Indentation

/U

PLATE 5: Subsurface Crack #5

Tungsten Carbide 1" x 3/8". 120 Wedge Shaped Indentor

Blow Energy - 55 ft-lbs

PLATL 6: ^ubsurrac? Crack #6

Tntioatan Carbido 1" x i/B". 120 -.-dee Shaped Indentor

IU

MMmfäm/täm

PLATE 7: Subsurface Cra^k «7

Tungsten Carbide 1" x 3/8", 120" Wedge Shaped Indontor

Blow Energy - 55 ft*lbf

PLATL 8; Sutaurfaee Crac:; «e Tungsten Cnr.ido

l" x 3/8", 120 V.cdae ShAMd Ir.'icnco:

lU

PLATE 9: Subsur:'..ce Crack -y Tuncssten C ..-. ide

1" x 3/8", 120 »edav ^r-prc: indontor Blow Energy HO ft-lbt

PLATE 10i .- J;JCU. ; .»C: . ra J-;

TUJI T J - •■>'■ c ■ ■" • ' I- x i'5", 120 '..'ederc r. ,; ; .dencor

14

üyc was uKi?d lo detect cracks. PUlfs 5 through 10 show Ihv results. Each of

thcac plates shows an indcntxlion corresponding lo a blow energy mrtrked under

the plate. In every cast- a major crack was produced roughly following the

centerline of the crater. Crack lengths were measured on the actual block.

In other experiments (at energies beyond IbÜ ft lb) crack photographs could

not be obtained because the blocks split open after two or more blows. In

these cases crack length was determined by /isual observation.

(c) Observationg

It The techrinues described above yield satisfactory measurement of

depth of tr-tck penetration. Cracks observed are several times

larger than the crater depth.

1. At blow energy levels of the order of 330 ft lb, the blocks split open

indicating crack lengths of the order of 4-1/2 in. (half the block size).

3. Figure 5 shows tlu plot of blow energy vs. crack length for the wedge

plotted o:i a log-lop scale. Thll gives the following exprcES'on:

*= 0.093 E0-67 {4)

for the particular wedge and granite block combination used in the experiment.

At thii> stage, the information generated htrc is sufficient to allow

order of magnitude estimates needed in design studies of impact excavators.

However, more reliable values of K and n should be obtained by conducting ad- ditional tests in the future, especially for different rocks.

4. Concluding Remarks on Subsurface Cracking

The work described in this section of the report shows the following:

(a) It confirms the existence of subsurface cracks which are several

times larger than the main crater dimensions.

(b) Spherical tipped tools do not produce repeatable results in that the

crack direction and size are quite variable and uncontrolled.

{■.) Wedge-shaped tools produce consistent cracks. The major crack

starts at the bottom of the wedge and progresses approximately in

the plane of symmetry of the wedge.

(d) The limited set of experiments indicates a linear relationship between

crack length and blow energy as (4) above.

?l < 15

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To illustrate the meaning of those results, if a tool ^vilh 10. 000 fi lb

of blow energy and an 8 inch long wadg« were to b« used, cracks as long as

10-1/2 inch in Bur« granite could be produced. This !• a reasonable su-.e

for use in impact tunneling devices. A bigger tool, of course, can produce a

larger crack and, therefore, is more desirable. Alternatively-, reducing the

length of the wedge will produce deeper, but les.s wide, cracks. One must

also keep in mind the possible cool wear which will limit the energy per unit len3

of the wedge. In the actual impactoi and tool design work to be carried out next' year one of the tasks will be to balance these two factors.

B.__ Ed§£_Fracture

1. Introduction

In this section NVC will examine one of the important mode, of secondary fracture; i.e., the edge fractu-e mode (see Figurea 6 and 7).

The problem of rock fractur. to ;.„ edge is similar to the indexing

problem in conventional percussive drill systems. The latter has been

studied by numerous investigators, including Simon. Cooper, and Stoneman8

Hartman , and Garner . fa „articular. Garner used the photoelashc model

technique and observed the tensile stress field which causes the edge fracture

Evans studied a more closely related problem. He .- nalyzed the two-dimen-

sional equivalent of the edge fractu-e problem, namely the action of a wedge

producing breakage into a buttock of coal. An equilibrium approach such

as used by Evans for coal (Fig. 6) wat not used here because hard rocks

such as granite tend to behave in a brittle manner. Once a crack is started

it can propagate rapidly in a suitable tensile stress field and therefore

the stress along the parting surface need not reach the tensile limit all at once.

The analysis in this report mil be based upon some recent work

done by Hatenyi ' . in the following sections, the basic aspects of the analysis will be explained first, and then the results will be correlated with experimental data.

17

r*.

R'- Wedge force

T - Equilibrium tensile force S - Tip reaction

Figure 6: Evans' Equilibrium Approach for Cutting Coal

IK

8 r-t a

ä 8 & V)

i I I 1

O £ 0)

fa

C 60 O T3

•H rj

U C

7

i

19

2. Edgg Frncturt' for ggtntgd Indrntors

In view of the previous considerations, the stress field produced b/

indentors is investigated with two specilic questions in mind: (?) Doc« the

stress field lead to crack initiation? and (b) can one gv.t come clues as to

the general shape of the final fracture? In wlnt follows it will be sh >wn

that Hntenyi's solution to the elastic quarter space sheds light on the two

questions for n pointed indentor and his quarter plane solution gives similar information for a wedge shaped tool.

An impact by a pointed tool in the neighborhood of a Urg« pielimi-

nary crack can be idealized lor the purpose of mathematical unalynir. by

what is called a quarter-space problem, as illustrated in Figure 7. Re-

cently, Hatenyi presented the theoretical solution to the prcbUn of a

point load applied at a distance, a, from the edge of such a quarter-space.

Here, Hatenyi's solution will be used to study the edge fracture problem.

Boussinesq sdved the problem of a point load acting on an elastic

half-space. Using Boussinesq's solution and a cl ver imaging technique,

Hatenyi derived the solution to the quarter-space problem in the fcirm of

a seriea of integral equations. These integral equations are too complicated

to be evaluated in the form of analytical expressions. He, therefore, ob-

tained the solutions numerically for four different values of the Poisscn's

ratio, v. Here we need not go into the mathematical details of Haten/i's work, but rather look directly at the results.

There is a mathematical singularity- at the point of action of the force

(x = a, y = z = 0). However, the scheme of successive approximation used

by Hatenyi in evaluating the series of integral equations is based upon the

distributed load solution due to Love. This removes the singularity and

- ^-^.

20

produces smooth utrcss distributions. The action of the moil in reality

creates a small crater with some state of qua si-hydros Ui tu- pressure

loading. Thus the Love approximation used by Hatenyi probably repre-

sents the real loading better than the mathematically singular paint

loading. In our particular application, we ire interested in o (Fig. 8).

Whun the maximum value of o^ reaehef. the tensile strength of thi: rock,

a crack can be initiated as depicted in Fig. 7-a. This crack will then be

able to grow and nach the free surface. The stress distribution shown

in Fig. 8 is for a solid with Poisson'«; ratio, v - 1/2. As v changes,

the stress distributions also change. Table B-l shows the stress fields

for various values of Poissonr, ratio. One can sec from the table that -

along the x axis assumes rather large value near the point of action of the

tool. For a truly point loading (^ would become infinitely large under the

tool. However, in Ilatenyi's solulion (in which the load is smeared out),

the maximum of ax occurs at x« 1.07a for Poissons ratios less than 1/3.

Table B-2 gives the peak fftlttM of o^ and the location at which they occur.

in this particular case, it turns oat that the stresses arc linear

functions of the Poisson's ratio. Figure 9 shows the plot of non-dimensional

maximum ^ plotted against the Poisson'? ratio, v. Thus, one can say

that when the stress maximum, q^. which occurs at x a, 1.07a. exceeds the

tensile strength of the rock a crack can initiate as shown in Fig. 7. From Figure 9 WO can write that

ov = k^- = [7.2 - i4.154v] -^ (5) Ämax a' * ac

where P = applied load,

a = distance from the edge, and,

k = 7.2 - 14.154v

Equation (5) can now be used to predict the load M which the crack will

start under the load. The implicalions of this are discussed in the next section.

3. F^rametric Relationships

The anisotropic behavior of rocks is well known. Even in apparently

uniform rocks like granite, the directionality of elastic and strength properties

has been observed. However, to keep things simple, the following discussion

is limited to homogeneous isotropic rocks. The effects of anisotropy are

discussed in somewhat more detail in Appendix C. (q.v.)

fl

■ »u; IV-J

HA I -;4: ) ":. SOLUTiOiN lOii KL/iSTIt: CU.MlJ .::l SJ'Af.}:

Rr.tio Streun i* tu';; X A;:is

5 * i i' ü.io;^ o.r.vs j. .;, (i.. «■ ,• l.:1, .)

-

'•)- ' j.i. .i I ■ UA---' i I :' : ■ o I.M-. ; ..(:.v;.: ..J.M;., j . „.;„,; ...... .

.,'•'*•! " i 0",;»; «'•'^•••' oir...' (».toir.: S.MI»! i.j-.,; ' <• i. i r . to ' ■ •••■•'!■•" I -0 :'-';i -ü.2S*.s - ' • I !

-- .__ . .. ' i I

, . o ,<■.".• '0.:!|vi I -» :t.'.;N , -O.sisi | ..(•..: .; ' . e.,.-^. ..•;.;,;; ..y.ovKJ ' . o.:

0.«-.^ j i/.lH': j O.'.'.'v ' Ü..VC-, ' :,.;'vij ! J K».% ' H I ... it.1

li •;

n . ..

c i • :

'• i ;-

Poisson's Ratio Stress AiDn;; Z Axis

„.. V, ''/' , ■"•l0,•, . ~0,',"■, . 0•0•,■,-, , ,,07,•, «"'^ 6.W»«i O.O^j' Ot :. o.i ..

t at < t

-•I» -ftot-.2J ü.t»;;::.; o.u>io; o.oi.*»' o.o:. > o.i>..:'>

''/• ! 0 i

O.wil« ! 9,mu

" -o! s>i •,-p : -0.3IS3 I -0 2Mi|

oo;jGi ü.J7:O -o.rtö.»; I-o.H'H -oirrc -ox:::

-O.W-C, ■ -O.ITH -o.O^S . 0 0S24 O.Ot-r. I 9.904*. OX.-)

' •- ;. 0 I -C.OTW. ; O.WsC ; 0.0746 0 UJIS j -O.OViO ! -0.i:,27 I -O.ir.Ji. ' -0X712

20 b

TAlMiK 1'.-/

PEAK ox STRESS AS PER HATENY1 SOLUTION

0.9Z

1.07-;

1.073

1.073

r.oii's. Ratio a2r. /P

1/2 o. vn

1/3 2.513

1/6 4.968

ü •

7.2

^ öu

V

STR.tSSLS ALCMQ X AXIS AMD Z Ax I *, I

Figure 8

STRESS DISTRIBUTION IN A QUARTER-SPACE

22

S D

;u u OJ l/l

^ (/.■

O #-^ ^i >• u. 4:

u H

X

t)

Pi o

/

/

(zV/ö) / yry''xyJ) s>|

'•.

. 1

t.i

The indcntalion characterislics of moil.? on rooks arc quite

complex and should normally be obtained experimentally. However, Paul

and SiKarskie obtained semi-empirical relations for wedge indentations,

and Sihaiski and Miller obtained these for a spherical-tipped conical

indentor. In both ^ases, the details of chipping action of the tool arc

taken into account in arriving at the relationship between force and the

indcntilion. These studies were oriented toward the percussive drilling

problem, rather than impact fragmentation.

To arrive at a more simplified parametric relaliorshlp between

the face, P, and blow energy, E, the following empirical expression

will be used. Let the indentation be a function of the applied load.

P 1 6 , rnax ,, ... • E = j Pd6 - r p % dp w

0 0

We assume the funcLional relationship beKveen P and E as followat

P = cEn (7) max

where c and n arc constants for a given pair of material a.id indei.tor.

The values of c and n will depend on the mathematical model rhoren

to represent the indentative process. For example, consider MM

following:

(a) Parabolic sprinp approximation for a wedge-shaped indentation

P » 62 (8a)

/. P oc E2/3 (8b)

(b) Cubic spring approximation for pointed indentation.

P« 63 (9a) 3/4

.*. P« E^^ (9b)

Other mathematical models can be used in a similar manner.

24

Ufiinf, the goaerftl e.ypft'.osion for equfttlon (7), one c.nu derive the ex

presr.ioii for maNJmum stress of equation (5) as follows:

kcE 'X

_T_ (10) max a

A single blow delivered at an energy level at which maximum n^ just

exceed« the tci'fiile atrength of the rock can cause a crack formaUon under the

indentor in a din ction normal to the x axis. This critical energy level is

given by: _ o,a _1/n

Once the crack is started, it will be assumed to grow in the tensile

stress region and reach tht- surface as shown in Figure 7a. Thus & roughly

tetrahudral shaped piece of rock is produced by applying a sirple blew of

energy E to the rock. Further, it is reasonable to assume (from Fig, 7a):

b " cia (12a)

h = c2a (12b)

where Cj and c^ are constants which must be determined exprrjmentally.

The volume of roughly-tetrahodral shaped rock pieces (as shewn in the figure) broken out is given by:

v - ^(2b)£. ^3,

where X is a shape factor. If one assumes a fracture curve approximating

a parabola in the x-z plane, X «, 2. We will experimentally evaluate this

parameter. From equations (12) and (13) , it is clear that:

V " V3 (13-a) For energy levels less than Ecr, the tool simply indents the rock

and produces a small crater. The volume of rock crushed is very small

in comparison with the roughly tetrahedral shaped volume of the rock fractured at E = E . cr

25

If Uw blow vrwrvy 'n. iucrc'isrc'. beyond E , Ihc volnnic removed is

not Increased at a given edge clistancc, a. Therefore one obtainB a «^t of

VOIOIDC imd energy ehtractorietict for ;i given rotk and t'.»ol as shown

■chematicnlly in Fipurcj 10. One can m>v. write on the basis of equations (11)

and (13-a) that the minimum vahic of criliial energy is given in

E 3 (V, min = "S-fi/nT <13-b) a

4. Wedge-Shfcpcd Moil

So far the discussion pertained to a pointed indentor. In this aectioa

wc will escnmine"wodge-ahaped Indentora. Figure 11 shows hchcmatirr.lly

the action of the indentor. Uhdei ihc« vc:l};c a crater is formed. A crack

which starts from the two opposite end« of the crater grows until it reaches

the frte surface. The chunk of rock thus broken out can be divifl. H into two

geometrical segments. Tiu- middl... aectlon is prir.matic, and the two end

portions similar to tetrahedra. If the width of the wedge becomes very

small, the two end portions in principle will not be much different than those

observed with pointed indcntois (see Equation 13). This observation im-

mediately leads to the following expression for the volume of rock broken:

Vw = y (2b) Y^ if wha = K4 a3 + K5 a2w (H)

where V^ = volume of rock broken by wedge,

w = width of the wedgo b ■ bi"7 = b2'2r half widtb of 'be fractured rock (see Fig. 11)

h, a - have the same meaning as before (as shown in Figure 7)

X, M = constants to be determined experimentally

Another quantity one car. obtain by simple comparison is the ratio of

volumes broken by a wedge and a spherical indenwox. Using equations (13) and (14), and re-arranging:

R = 1 lT2bhaM^)wha^ wedge (15)

.T2bhaJsPhere

One should not infer, at this stage, that the bigger volume produced leads

26

—J

a-'

v.

^

-l,^ A-W

L— !

^

li)|>

kj

— • V

t. t,

.. I

r. :■:

N

v T

?

I c r

C •r-l

ki UJI^

11

+) U

» % C\J >

/ : !

CL

s

fl

c o c •r' C V. ■-* r. *i c. q

i q o o

(-

c.

c/: o

0 s 0

4J o <

c 3 r

28^

p L'Ct P = v7 bc thc pcnH force aPI,,it!d PC unit length of the wedge.

The action of the W«4ffl produces a tangential wedging force F , which in

norm;«! to P. This .orce is far mon; effective in producing tensile

strcs« than P itself. The solution for thc line load Ft is again singular.

*m**r. ,v. ca., write ft. .ta.OBM expression for .he for,., * ,„., .trcs8 as follows:

F o = 6~ = S S tan a xmax a wa (16)

where a ■ half-wedge angle.

Using the oncrgy rdrtionship P = cEm, one obtains the critical energy in the following forrr.:

- cjj.wa .. 1/m Ecr-w = [ cPta'naJ in' lb (17)

The confitant, ß, will be determined operimentally.

w ^ a One must note that the two-dimensional approximation is valid for

Fr.r w « a, the distinction between wedge and the pointed indentors should vanish. For our application , however, w »«a.

5. Experimental Verification

The IRRI droptower facility was described in the semiannual report; a picture (Hate 11) is included here for reference. The experimental

work was carried out by Messrs. C. Sliski and L. Yaro«.

For the experiments. 18 in. Barnc granite cubes were used. Each cube was suitably mounted under the droptower in such a way that the moil

would impact at a desired distance, a. from the edge. The moil, an

example of which is shown in Plate 12. can be raised to any desired height

with the help of a hoist. After raising it to the desired height, it is released

by a pneumatically actuated release mechanism. Aluminum guide collars

and guide posts prevent side-to-side motion, tilting, and rotation of the

Late Hi Droptowci Facility

nt

Plate 12: MoiJ and Point

29

moil as it COJTU'S down ! "ri '■it»' r.i<' ro.l< 'J'i.v '!.• i^ liuli-til ( . ■■■ i i j'<

bluv. energy) \.. - varied o\ r .• witli" r; n; <• ij-. i-M 1. chj.i-, ' »1 rd <•• . .-.

ol^.c'.vJ tu !>•• r. ■: n U. Th' t'irvcHonaüty (bcdttri . j.'.•..»;■.) (■ ■■, nnl

(urmincd in all cabus, Thitjs ;hc- v, ••1!-- may be Lni« rprot* I . uvv.i'aj

cakun ovi r ill dirocliuna,

A direct obuorvrttion of crilic;.! . n -r^y ( . 'n« jiroV'1 Llistic t.. cjucs)

is very difiicult without ptrj jrmlng 'i ^•"^';, numbc-j of bxp^rimentst. io '.i«ii>

kh« cost within limits i nd ^'Jll allow <) good catimi In o' critical one» ;•. the

followlnpi ; lothod v.:. . ueed. At each odge du-t; •. <■, r, tlu- di-(i|> hcip i ;;

lowered to a poirtal which :: dingle blow will u*r. >lly n(jt be ;.I>lr to r;-. .• • edge

fractuiCi Thor tu&ts \ «^r«. run at tillghtly hijjhci rnergy levrla where i r to

80'/i» of tlir tir.K;;- i» : :-.;jlc hlrr.v will break oui . chunk. TWs ".J'S th" •. . »»»umed

tobe the critical onorgyt in nome caac» ealin;:'tfr. LOI;1'! bs. m^df u*. by

uaing th<' oxperimonter'g judgment.

(el Spherical»'fipped Moil

Three solo oi experbnents vyorc conducted using a 5/8 in. di- <. ..i> r

splicricnl-tippcd moil si edge diatftncea of 1/?. in., 1 in., ai.d Z in., re-

spectively. Tüldeö 1 through 3 in Appondix A shu\'. the blov energy« J . the

number of blows, N, required to fracture the rock, the total blow energy

(K x N), and the weight of the rock removed. In addition, the dlmeralOBl b.,

b?, .-i.nd h were measured for «.ach brol.cn piece of rock. It was observed

thafo/ten b, and b, would not be cquc>l due to a variety of reasons auch a»

"buddinj- planea" being oblique to the cdp.c, moil not hitting pv rfcclly i t

right angle and inherent flnv.s in the rod;. TVsls in which b. r- b2 v . : i-

judgtd to be more meaningful than when b. / b^. T'' take'lii*"« into acCDunt,

a statistical weightir.p paramtitcr was used in reducing the data. Thi?

weifliting parameter, i, consisted of the ratio of the geometric rnear. to

arithmetic mean, i. e.,

a V^ CU)

when b. R» b-, U) so 1, and when b. * by or by « b., uu«» 0.

f The strength of rock in the direction normal to the bedding plane:- ia larger tha: the other two directions. Thus on the average 1/3 of the limes or.t- should expect the rock not to break. Therefore we used a bO-SOTö limit.

30

In some indtances, due to poor aligmm-nt, etc., om: KHIC of the

fractures extended byond the block tsi/.e, i.e., b. >. 9"or b > 91 These

tests had to be discarded.

This statistical weight, X', WHS used to average b., by, and h, and

the weight ot the rock removed. The c-.vcrr.ges, means, and ntandaid devia-

tions were calculated in •Ach case. Appendix !J shows the results of slatis-

tical evaluation. In each case ^^ confidence limits are calculated for each

variable. In Figure 12 described bslov* the means arc shownby a circle

and 957o confidence limit is shown by a bar.

Observations; Figure 12 shows the plots of the averages of b (it is the- com-

bined average of b. and b.,) and h It is clear that except for a small offset,

b and h are linear funclione of a as expected by equations (12a and 12b). Our

indentor was not a true pointed ind'-ntor but had a 5/16 in. radius, this

probably caused the offset. The small offset in b and h leads to an error of

0.67 cu. in. in volume. When corrected for this error (by subtracting 0.67

cu.in. from measured volume), the averaged volumes of rock removed vary approximately as a cubit function of a as shown in Figure 13,

Figure 14 shows the log-log plot of the critical energies vs. edge

distance. From the slope of the line passing through experimental data points, 1 84* it was estimated that E «a * cr

3 Finally, Figure 15 shows ihe plot of specific energies in in. lb/in. ,

(psi). Ihe slope of the curve clearly shows that the specific energy varies

inversely as a, as one would expect from equation (13-b). In conventional

tunnel boring practice, the specific energy is a sizable fraction of the com-

pressive strength. In the case of edge fracture the specific energy is orders

of magnitude smaller than the compressive and even the tensile strengths.

(b) Wedge-Shaped Moil

The experimental procedures used here were the same as above. The eff cci

of wedge angle, although important, was beyond the scope of this work. It

was, therefore, decided to drop the variation of the wedge angle and limit

thij /ear's experimental program to the determination of the important

2 14 ♦ The first two points gave E «a * or nft*0.94. This variation is cr probably due to the spherical radius at the tip of the pointed indentor.

31

•

• G-

• • 1

-

4-

<

2-

t.C I«? 2.0 i-s

FIGURE 12; ROCK FRACTURE PARAMETERS

POINTED TOOL

I *?.

I-

:

I I i:!

Ji

[ 1

10- c

3 - u

it I "

^-

■• 11 • i

t r ■ :

I ••

1

;

; •....

..

..(... .

:! . • iVJ 1 . • : :

i-^T-

■ ! •

O Volumes measured for pointed tool corrected for 0.67 cu. in. offset error

•}::: . •; • ; | :.:

i .1 utl

I m Volumes measured for wedge-shaoed tool

• 7 • • t

a ■ inches

i . i ' « »T • 7 t. • (0

iLXJ • • T • •

FIGURE 13: VOLUME OF ROCK REMOVED AS

J3

a in inches

O

B • • <

Slope

Slope

.:;••:■

= J.88

= 1.47

» 4

FIGURE 14: CRITICAL ENERGY AS A FUNCTION

OF EDGE DISTANCE

34

C'-l

r. ... --. J3

Vv >

.,\ \\

•

•

.

.

I •.

... .. .1...

•

... .. • 1-—• I

• • • 7

• * -

...i....

1 »r \0A

. :• • -

■ • •

. . .

. ....

I.: i .^., m . ..

i .i-

11. • 10

• -• ■

•;

I »- ... i

_

■

. ; . :

...., .. ...

■£iB.- * • • T

a in.inches

FIGURE 15: Specific Energy as a Function of Edge Distance

3ü

relbtiuru'hips bclv.i-i-n critical iTici'gy, volume of rock rfmovcd, und the edge

diatanco, a. In al) tests, a wodge of 90° included RngI« was used. The

Weighting futictiotiB used r. re the following:

tt - Ü when b. > 0, or h. > 0.

where bj^ - b. - -j

Once again frftcturee breakinn into oiu- cl the corjiers wore discarded. How-

ever, it was found lhat even when ttni fracturee prograei ed close to the

corner (j..ty within 1 to ii in.) POmtwnal larger pieces were broken out than

usu-il. In Figure 16 the plotr of h vs a and h vs a are shown for the wedge.

Notice in the plot of h vs a the point »la « 2 in« is well iibove what would be

expected because of the pro.tir.ü-;' of T.-c fiacture to the corner:-, Wc there-

fore consider the doited line pciftfinfi through th( three points erronooae and

the solid line passinf thioi.j-h the first two points to be the correct one.

The waighted averap;cs, m<--anü, standard deviations, confidence limits, etc.

arc obtained in the same n-.an.vr as above (rec Appendix B). Tables 4, 5,

and 6 (Appendix A) show the smntnary of observations.

Figu-es 13, 1'!, 15, and 16 ehow the various relationships between

the variables for the edge fracture problem.

6. Edge Fracture Conclusions

It is clear from the text that an understanding has been reached in

the area of secondary fracture. The principal conclusions arc as follows:

1. There exists a critical level of single blow energy at which a piece

of rock breaks out from th? edge.

2. The volume of rock broken out is principally a function of edge distance

and tool shape,

3. Hatenyi's analysis can provide a basis for the crack initiation in edge

fracture. More rock testing will be needed to prove the variation of

critical energy as a function of tensile strength and tool wedge angle.

35a

4. Basic geometrical relationship;, between b, h, V, and a derived in

the text have been confirmed cxprritmntally.

5. The 2 in. MfOdge-thapod too] proved to have lower hpecific energy

tlum the pointed tool.

6. Low specific energies arhieved during the teL-U; hold a promif.e for

tunneling system applicat'on.

7. Summary ResuIts of the Cdpe Fr.n-tirc Tc»tg

The numerical relationships obt/iined for the set of tools and rock used

during testing are given below:

Pointed tool: b r, 1.84a; Vw5. 3a2,72; Specific Energy =. 96a"0'88

hfc2.7a; E «12. 5a1'84

cr

2 In. ,90* wedge tool: b ««<2.2t>a, hv 3.3a; V ^ 12. 5a2*43

E * /Op.1*47; Specific Energy ^ 67a"0* 96

V

''

)6

/ s /

/

^

/ /„

s /

■■ ■•■

Cr-- -

c Ij

1 . im

■ ~- T

s

/> Krrur clu«' l«> V.\v\ effort« not Hccounl^d

&r* "—• -Corr«rted b cu rvf

o~^S <s

s -y

r_ —T • C 1.3 2 0 lb

a

FIGUrC 16- ROCK KRACTUKK FARAMKIEKS FOR I IN. - 90' WEDGE

'..

h, Int rot! mil on nnt' .'irt t FipM ''. . t

The purposo of the fit'Jcl tt si» cr.rrlc-cl mit < :■■ thJK prog .i.\.>

to gain oxpcrlencQ with in-sitn im]* « ' ioc)- f\. v.itltv i . hard uxt' :v<;

fornialionj, utilir.iiv! avaÜAblo u^uipinc-i I,* To .'. '< . :;'trc' field t.. '..-.

tjbilin- six weeks duration bxive been carried out, iar* ca].ablc- of

delivering 1000 ft lb/blow and iOCO ft lü/blow ..-. • ■ .v. i) le Jur all llir<.

field Uz{.<, while a 1J,Ü?0 ft lb/blow JI.IJ. : •» -..;.• . vfaiiable for lh

tb.r<l t^st. The various moils used are i l\o\ ri In Piate* 1 • and M,

The firstfirl- tc^twa« rcpurti-d :•) '.}•• ;«.'->ni.:.' .I Kc|K>rt. Al iin-

time o! iho test, two impactors \ •••• aihibb-: ;. eei >n< r« ';•! 1000 ft lb/blow

impacto/, th« Hobgoblin 1000, eq»»'pi • ' will ■:• i— - .• •• • i moll poini i, and

an espcrimuntal 3000 fl lb/blow iniji etor, :•• • D»ii;o»! 101», equipped ui.)-. ;.

blurt tool. The field test was coudiu ted .; C". SJ 1. v.lio made the followli

ovner\r> Uonfl:

{l| This teat demcmatralcd thti will-« .-•. pod TMOü it.

more productive th.in a Mui'i or co:ji<.. 1-. haped moi).

(2) The 3000 ft Ib/bJow impactor was more productive tlr a

the 1000 ft lb/blow imjH.ctor,

(3) Due to the high atrengtli (eomprcaaUe stret^th *10,üü0

p«i) diabase fonnati» n lound i-.l tlie quarry usc-d, avallabl«'

tools could obtain only a limited amount of rock breakage

• off the face.

2, The Second FieH Test

A second field test was conducted by C. Sliakl during the period

October 13-19, 1971 at the Shahmoon Indubtries Quarry in Mt. Hope, New

Jersey. There is a granite gneiss formation in the quarry with rock

properties as shown in Table C-l. Testing was done p.t B rock face which

had a layered structure with a large number of small crack« along the rock

layers. The following equipment was ut-ed: a standard Ut.ihoc 117, a 1000

♦ TM-7111: "High Energy Impact Rook Breakage Research Program -- Semi-Annual Report," October 1971, p. 23.

S8IU

ft lb/blow imprnctor with u BtcJlitf-coüU-H wedpt! too), a carbide butlv..

wadge tool, and a spado tool, and a 3000 ft lb/blow Impactor aqoipped wWh

a blunt point.

TABUG C-l

Comprussivc SlriMi«'lh - 36, 000 pui

t)tMi8ity = 3.05 s.^.

MinrraU ■ Granitt- gneisa, having a major mineral constituent of Rornblanda

Hardness =5-6 Moh

The brit.f axparierice with ihv several tools gave an Indication äR which

tool vould be better in tcrmb of efffctive rock removal and longer \vc?r. A

blunt tool on Hia 3000 ft lb/blow impactor was not very effective In romovln«

rock. W'c did not observe any subsurface cracks by visual inspectior.. The

stellite-coated wedge tool lasts approximately twice as long as the bf.sic

wed^c tool used previously. It, too, however, soon blunted and becftne inef-

fective. The enrbide buttons on the carbide button tool broke quickly, and

again the tool blunted to a large ineffective radius. The spadu-shapec tcol

gave the most promising results. This tool has I in. thick b'ade , and

therefore, as the tool wears the tip radius does not change much, ar.i the

bhapc of the tool is retained, (see Plate 13) This tool was the more effective of the tools and lasted through the test».

The commercial Hobgoblin 1000 ft lb/blow impactor did not develop any operating problems while the experimental 3000 ft lb/blow impac:or

cracked at one of its welds. It produced only a large crushed rock zene

beneath the blunt tool with which it was originally equipped. It was observed

that this rock broke out more readily th?n the hard diabase rock of the first

field test. C. Sliski estimated lhat 150 blows removed 158 pounds o: rocK

from the face for a tuughly-estimated specific energy of 142 psi. This

removal was achieved by edge fracture using existing surface cracks.

Plate 13: luuu ft. lb. Impactor Muii Points

(iiom left to righti cunc. carbide ball tipped cone, spade, carfcicio ball tipped wedije, and steel wcd%e with 12 In. ruler ghown on spade)

t&L

S94/

Several largo boulders (aj)j>roxiinalcly d'vl'x-t') wore also usi-d to test

the Impaciis^g incthod. The bouldcra were solid and unweathered« The

bouldera were split with blow .s, both parallel and perpendicular to the

favorabl.- dlrecttons. V.ith th« Hobgoblin tool placodr.tthncc-nferof tlurock, it

was possible to split tli<- rock with about 150 blows. A 1 in, deep crushed son«

would lortij 1 .-fore ■plittiltg would occur. Once split, the rock could be

broken furthe,* with mort« ease.

Some problems were encountered daring the second Hold test. The

Demon 100 hydraulic impulse breaker cracked at a weld before testing

could be conplcted. The Standard U.iihoe 117 boom did not prove lo boa

good mounting lor these impacto-s. The reflective shod; from the blowi

resulted in broken hoses and lines. Also the rock removal rate was Impeded

by the awkward positioning of tie Impactor. FHtture impactor mountings should

Provide for turning the impactor about its axis and changing its direction at

a pivot point closer lo the impactor.

^. The Third Field Tctl A third field left was conducted by Lee Yaros during Ihe period Jdimary

10 to February 14, 1972. The time opent in the field totalled about two weeks.

During this time the weather was bad. On two occasions there were snow and ice

storms preventing accessibility to Iho working face. The equipment consisted

of a standard Unihoe 117 with the Demon 100 and Demon 300 impactors. These

impactors were of 3000 ft lb/blow and 10,000 ft lb/blow energy respectively.

The Demon 100 was equipped with a steel spade-shaped tool with a wedge-shaped

point. Likewibe the Demon 300 was equipped with a steel tool of the same shape

as the previously-mentioned tool. The Demon 300 was also equipped with a

carbide insert tipped tool with a wedge-shaped point (Plate 14).

The new spade-.and wedge-shaped tools were more effective than the

blunt tools previously used on the 3000 ft lb/blow impactor. The tools pro-

duced smaller crushed rock zones, large pieces of rock were removed,

and the crack direction could be determined by the operator. The steel

points made of AISI 4340 steel showed minimal signs of wear. The carbide

Plate 14: iuuo iina luouw it. iu. Impnctui and '''üüIS.

From top lit to i i jht: JO-JU it. lt.. i ;;.}.'.irtoi with steel spacic -WCCI9C point<-u tool; IUVA-O ti. 1c. Lmpactor with carbide tipptd wednr tool, two blunt tools; und a

steel spade -wvdye pointed tool.

tHi

404/

point o„ ihr 10.000 ft Ib/bJov lmp.clor showed „o .ig„a of wear, chipping.

or cracking after doUveHng :<0 blown. The 10,000 ft «,/blow Impactor waa

much more effecHv, thai, th. 3000 ft Ih/Mow impactor with chip« of rod. flying

off with each blow. Tic op«rator had to protect him.eli from thos« flying

chips. As a rough caii «ite, the 10,000 ft n./hW Impactor could effectively

remove fron, a ledge in the face (in the aecondary breakage mode). ■ 10 to

20 pound rock with a ..„gl« blow ladlcatinjj a apocific energy of 71 to 142 pai. 'Ihis unM is ahown in Plato 15.

Some observations could be „.ado from the third field teat. The 10,000

ft lb/blow Impactor waa much more effective than the 3000 ft lb/blow Impactor

in proofing secondary breal n,e. A movie sequence of the imp.ctors opera-

ttllg in the secondary break.;-, mode has been made and forwarded to TCMKC.

The tests were inconclusive in demonstrating the Impaclcr'a ability to product

primary cracks in thin competent granite gnaiaa rock. The ability to see

the.e crack, waa hindered by the dirt, duet. mud. and water present on the

reck fa^e. The ability to.induce crack Interaction by geometric «pacing of the blows was, likewise, inconclusive.

Several problems of a practical nature were encountered during the

tnird field test. The four bolts used to hold th« tool point onto the piston on

the 10, 000 ft lb/blow impactor broke. Th««« four bolts were replaced by

eight rocket head bolts which lasted for the remainder of the tests. The

Unihoe 117 ooom could barely support the 10,000 ft lb/blow impactor due

to its v.cight. To keep the machine from tipping over backwards, weight

had to be added to the front bucket. The greatest problem encountered was

the durability of the impactors. Both impactor« cracked at various welds during the tests, stopping further tests.

ii Lab Field Tests - Five Foot Granite Cube

During early March. 1972, high energy impact rock breakage tests

were carried out by L. Yaros on a five-foot Barre granite cube. Ihe

equipment used consisted of the Unihoe 117. the 3000 ft lb/blow impactor

equipped with a spade tool, and the 1000 ft lb/blow impactor equipped with

a blunted wedge moil and a carbide-tipped cone moil.

Plate I'): Field USL ^ i l^.juu ct. n 1 H Ol < .11 v.' •■..■■ 1.; •!,:...; i

Hop., N^ w J. i • ••.

InipacLi »i iiom Mt.

Vf

•n

TOO! one rt»näinii:cl <if soni«.1 oduu fracture tusta usins the 3000

U lb/blow Impactor. Thcs results arc given 5n T&ble C-2 bil«»\v.

TABLE C-2 r Wuigbl of

7 lb. 494.0 psi

13 lb. 265.0 psi

162 lb. 62.5 pbi

13] lb. 105.0 pi

Figure 17 shows the posiUon of Ih«1 pieces of rock removed during

the list. This le.-i Rave confiden'-e th^t »he data obtained o» tJje drop to\v<:r

yields reiJSonnl»lv qt ntititrt liv<> cstitnal« s. No effort was made to determine

critical energy and specific dimensions of breakage.

Test two was to do'.ernnne the effect, of closely spared blows at

3000 ft lb. blow energy (see Figure 1C).

Sequence Number a

in b]

1 <:.•• 1

2 3" 1

3 >3" z •1 5" i

Blows of 3000 ft lb were delivered at the center of the block within

the two foot circle in a random fashion. Some of the blows were delivered

parallel to side A, others were delivered parallel to side B.

TABLE C-3 Blow Parallel

Sequence Number Number of Blows to Face

5 7 A

6 8 A

7 10 B

8 10 B

9 20 B

After each sequence of blows, the rock surface was cleaned with a

wire brush, and an attempt was made to find some cracks. Although no

visible primary cracks were observed, a crater 2 ft in diameter and approximate!

■it

— 2 r-T.

t:.

A

B

k FIGURE J7: PRIMARY FRACTURE TESTS - b FT BARRE (2RAKITE CUlilJ

V

FIGURE 1«: SECONDARY FRACTURE TESTS - 5 FT BARRE GRANITE CUBE

43

1 in. d«:cjp was formed in the cub« by th^ rcmOVftl of 1/2 in. to 1 in. chips

of rock. From lhaso rough o«timatosf ;• ■pvciTic enurgy removal rcitc of

4 370 psi was cstiinatcd.

Duritig the laut srquenco of tcbtc, the 3000 ft lb/blow impactor

cracked i\t its welds.

With the ecperimeatftl 3000 ft lb/blow and 10,000 ft lb/blow im-

pactora both dmnaged, an attempt was in;tdi! to use- the commercial

1009 ft )h/blow Impactor to impact a five-foot cube granite block with

carbide-tipped cone ai.d wedge moils. At this low energy the moils

pulverized the rock instead of removing chips andwere therefore ineffective.

(A roughly estimated specific energy removal rate of 32,000 psi was

obtaii.od .\ hen the 1000 ft lb/blew impactor was operated for oiv-half hour

with bknvi randomly spaced within the two foot circle.)

44

5. Field Tct.t Cone 1 usiony

1. A siKid« tfaipod tool is bcUcr thfta other skap«« because the erne?:

direction can be controlled by tbu operator, and its v.cav cbarac-

tcristics are better than olbcr hlv'i!*<:•!,.

2. Secondary breaKigc rock »cT.rv.il could be done effcetivoly with

the equipment availabie.

3. Primary cracks could not br. readily observed durinj» the field U.si^,

and proof of our ability to inducv Hum with the field test equipjrunt

available is inconclusive.

4. The higher the blow energy avrilable, the more effective the

impactor from the standpo^t cf rock removal rate.

4S

III. riKLD TEST PrvOlM.K?Nlr>

The problcniH generally encountered throughout the it^l« v.-«re

m.Tinly concerned with the maneuverability and clufability of the equipment

used. As has been irunlionid previously, the boom on the si. m' -rd Uni-

hoc 117 docs not readily allow accurate and eaay positioning of the impäctors,

nor can it handln the shock of the Unpueting blows. However, durability of

the experimental Impactors was the majot problem encountered, «lad the

3000 ft lb/blow PT.d 10,000 ft lb/blow impartoxs b«:fn able to with«tiind t! c

punishment of the tests longer, a small tunnel could have bc( n made in

the qu:.rry face at Ml. Hope, N.J. This would have allowed us to j.vike

overall specific energy measurement»; and would have indicated that

primary cracks were being induced in tho lock.

46

IV. Firn IRK PLANS

At th« oriel of Che fir at year tin* follow i; commento may be ro;.tlc

with ih( vii-w of ftpplyini; high energy imp-ict tool* to .1 practlral hmneling

nysii IM.

(;.) R.iDif r ■ubttantia] blow energy is required to croatr largo BubAurface

cracks. For examplei Ihn theoretical work indicates that a 10,000

ft >b loi>l (8 in. lonp,, wodge-ahapod) wo..Id rrt-ati- a crack 10 in. to 12

in. deep in granite. This ic probably just into the lover end of the

practical range of application« In harder rock*1 larger impact tools

•.vllJ. bo needed.

The rests also showed that a wedgc-phaped tool was brllcr than a

pointed or blunt tool.

(b) Scrorfary fracture showed the promise 01* high energy impact breakage

to at'.'in low specific energy in tunneling. Here flso the wedge-slu»ped

t'>ol was found lo be butter than the spherical-tipped pointed indentor.

(c) The field testing showed a need tor a more reliable impnetor and a

better mounting lo obtain maneuverability for the high blow energy

tools.

Plans for the Second Year

The second year as planned ends in December 1972, and thus has a

duration.of eight months. To utilize the time most effectively, it is

planned to concentrate work in three basic areas, namely:

(a) to re-design the 10,000 ft lb impact tool.

(b) to perform pertinent r ck testing with rebuilt equipment as needed.

(c| to examine some interactive considerations of strategy and mountings in order to design the tool.

Field testing with available tools, although useful, is not contemplated

for this year due to lack of a reliible tool in the useful blow energy range.

However brief tests may be carried out to gain lesign information.

I'-

ll in Bugg« Bted, Ihercforoi that the work »houlfi be divldcJ ruuglily ni

follows: luMn % >-,r l^^•'■>,•.. r< i..

■i

/'

10,000 it lb t'^ol, rt-d»sißii f>(>

and rebuild Sifting -»0 000 ft Jh l< .>J 20;:

Rock tealiiiB a«>c' locil~&h»«i>ti ^QV tcs;!'^-

The design effort cl.ould include con. Id. ration such as whether to

use impaelirg jniitoti typ< or hurlcd-hil ty,*- d.-vui-, wh."»! structure r • t

be v.std to aupport th< too!, and the bJ.Bic bydir; ul{< ol the ayatom« Weak

linkst- obhcr/od in the sys:. in durii flnld li»l mu»t be eliminated« The

tool OCBJJ.O work will be done In conirulUllon with Impulr < Product.'.

CornoratioM, and Pro/. Voltsekhovaky in Our U.S.S. K.

Rock lesttag ahuuld be done in a differcnl rock thn granite. Sxiitabic

rock will be chosen, and after approval of Ihe Buraan of Mince, 30 blocka

of 1-1/2 ft rub« will be obtained. Ion bloc'..- v.ill be used to dctermi :e sub-

8'u-facc fracture, and twenty blocks will be used for ed^e fracture.

Fir? 11/ some thought would be given to available mountings and

Sfcondary systems. In particular, the available crawler mountings w'll

be studied to estimate changes needed in these for future field trials o:

10,000 ft lb tools.

The outline of this proposal effort hat» been forwarded to TCMRC

for approval.

* These include (1) welded joint failures at the side restraint due to

side loads. (2) automatic recycling, (3^ bending and transverse load failure of the tool point.

v« R»:ri.k. NCKS

1. FalrKtirnt, C. ami W. I). I.i.-. '...i.:..-. "SOUK I «I-.•..:;.!, H ^IUJ DfvclopinontN in Hard Kuf-k lirillii > T'ru.v^t, ., " t-, .,,,.,:; Siyth Ai.nual DHti md IIJ I ... i;...', i . ," . Minucsuti• (uetu'ü ;rJi-j.;, j ,. ••).}.• • . :•.

2. Rrjclinviih. D.H. "CorrclMicn of K . L)l;-p) .. • I n.il.- . r. HiysicaJ PropertU* of Rod ; .r Pt-rci vu liiiUluf; .Sy*f. " i'"-".1." •■'i jcs. ' '.. ■ ■ (i; .- r»i__)'' . ' . i; ; «• ";.v'. •. .c.'1 .'•_'■.:.• i'<!»^v- 'J, c. : . ;. ', u . . ... jCiTi ••i'..,' Pcrc..i,,(.n (196 ). pj». 33-.6],

3. Pun», ;•.. andO. L. SiUar*ki. "A i'r UMIII : i:. . . of Si ••. Pcn.lr. !»on by a Rij'.itl XWdyv into HriitU< Mmorial " "'•.r Tranv Lions (19: ">) p;>. 37.'.-/!. >. — - ■

4. MilK-r, M.H. M.<« P.!.. SiK- i U. "O.. U, )•..;,.}..,•, , t.f l>t.c|%

bjr Three-Dimvn ionaj Lidentom." i-.!. J. of Ro I c-hnn'ca >nd Mining Sctcrcc». (l-?6:.}, pp. J7" . .

5. Pciul, B. and M. D. Citngal. "Whj C..... ,!•«...;•...• I.,. in t,n brill liits Produce Tensile Splitting in Keck." Paper No. Sr£23<»>.,

6. Aquino, C. P. "Prediction of i-ractn •<. Duo to a Hnnnnet StHklna anritiUMHlfSp.cc" (»Vl.ruary, 1971). Private commonicakion from Hi li Lahs.

7. Hoilcnbtrc, Joel W., Cheater J. SlihJ i, and MUIU-K! D. GanpaJ. Hinli Knargy Imi^ct Roch nn-aka^.c« Reaearch Progrnin Stn.i-

Annuni Riport. " (Octobar, 1971). Sponsored b> AtKvmcrd Ri- scarch Projects Agency. liureau of Mines Contract No HOtSOMS.

8. Simon, R., D. E. Cooper, and M. L. Stoncman. "The Funda« mental« of Rock DriUiag. " ProMcnliri at S^rin^ Mc.-Ün« of ]' slern DLstricl of API, Divn. of Produclion, Cdumbua, C.'i"."7\p7ir^T^* ^7, 193Ö.

9. Hartman, H. L. "Simulation of Pcreussion Drillinn in tl.c Labora- tory by Indexed Blow Studie*. " Proceedings of the Is«. Conference on Drilling and Rock Mechanics. Univ. rsity of Texas, (l^oTK

10. Garner, N. E. "The Photoelastic Determination of the Stress Distribution Caused by a Bit Tooth on an Indexed Surface." M.S. Thesis. University of Texas, (January 1961).

11. Evans, I. and S. Murrell: "The Forces Required to Penetrate a Brittle Material with a Wedge Shaped Tool. " Mechmical Proper tics of Non-Metailic Brittle Materials. Inu-rsclence Pubhcations.' (New York, 195Ö).

49

1Z. H.itrr.yi, Nf "A G<moral Sü1«<I«»M for EIHSUC Quarter Sphc«, " J. Appl. M. ch. (March, 1970}. j>p. 70-76.

13. Hntcnyi, T.i. "A Metiiod of Solution for the EltiHtic Quartor Plan«-." J. Appl» Mech. (Juno I960), jip. 289-296.

A-l

APPENDIX A

T.Tbk-s J Uuoujji 6 {-.ivo the ■ummary of

obscrviitionn jTiadc flu ring tlu- drop lower lesti 3 foi

edge fraclurf. Blow imorgy la in ft lb and the weltfhl

of the rock removed is in povnds.

Tablü a Tool

1 win. Spherical, 7/16" diu.

2 1 in.. Spherical« ll\f, ' ;:ia.

3 2 in. Spherical, 7/16" dia.

4 jin. 90* Wedge, 2 in. long

5 1 in. 90* Wedge, 2 in. long

6 2 in, 90• Wedge, 2 in. 1-ng

Quantities b, h, and volume, and the statistical

evaluation can be found in Appendix B. Determination of

the critical energy has been explained in the test in

subsection 5 of the chapter on Edge Fracture.

so

A-2

TABLE 1

r.nr.M, my C»r DROP VC(>!V.P.

NO. OF BKXvS

WAL BLOW ! •■ ICV KIKJ NO.

BI/.»V;

EJIGRGV

WEIGHT OF ROCK

RDMOVTD

]63 7.92 ^ 15.34 0.113 164 3 23.76 0.194 165 2 15.84 0.163 107 2 IS. 84 0.15? 163 2 15.fM 0.0533 170 11.9 1 19.82» 0.245 371 2 23. a 0.155 VtA 11.9 0.0707 17? 1 11.9 0.146 162 1 11.9 0.0706 154 47.5 1 47.5 0.157 155 1 47.5 0.256 156 ] 47.5 0.181 157 1 47.5 0.121 15S 1 47.5 0.197

♦ Smaller Second ßluw.

*l

TADLE .'-

SUMMARY _0:^ J i^OP TOn.H TEST '• T 7

WIIGUT C: 1« t 11 1

BLOV; NO. ()]■ TOTAL BLOW I:OC}: RVJ-' \U)0 JUTC!

31

'.GY )ii-o>;.s BNERGY ii-ro1 :-j

Ifjl» .'! 31.4 0.25 if.:- 31.4 0.?5 14'i 2 62.8 0.75 15.» 62.0 0.50 Uii 62.8 0.70 l.i :i 47. .5 47.5 0.75 141 47.5 0.50 140 47.5 0.65 14 J 95.0 0.60 14-; 47.5 0.75 i:<;» 95. ,0 95.0 0.35 13'J 95.0 1.00 13S 1 95.0 1.50 137 95.0 0.25 13O 95.0 0.50 13:1 • 95.0 0.25 13'.' 95.0 0.35

^

A^I

J'A 1 ILU 3

BUMMMjy r. • P .TO'^KU '■■'■':V.

RUN KO. BLOW

.UK 5

NO. jrr

OP .■:r

TOTAL DLCV; WEIGTIT C

ROCK

'» 1045 4.0 10 104^ 10-': 5 11.0 12 230 23';J 3.0 13 238 1711.5 14.0 41 23il 238 5.5 42 1«;0 190 4.0 .13 143 14 3 1.0 44 143 572 7.0 45 143 143 2.5 40 14 3 143 1.5 47 1^3 143 2.0 <0 190 420 12.n 49 95 285 6.5 50 95 475 3.5 51 95 285 6.5 52 95 190 1.5 54 238 238 1.2 55 230 476 12.0 56 238 476 1.15 57 238 238 8.5 58 238 574 3.5 59 238 238 2.75 60 574 238 1.75 61 520 520 4.5 62 520 520 0.465 63 520 520 3.0 64 520 520 8.5

f'3

/. -;

TABLK i

Wl ' ' 0" DIlOI TO :.\/:_,TV

WEicrn C BTiOW MO. OK TOIhh liJAM UOCK

RUN i:o. KVi:;- • BLOW.«] I." ' '" ' RKI

17D 19.0 38.0 0.318 1B4 3E.0 0.29^ 18^ 15.0 O.OCC let 90.0 O.l^ii in9 38.0 0.324 177 21.A 50.8 0.11:- 17ß 127.0 0.239 xac 25.4 0.15? 181 25.4 0.177 li? 25.4 0.174 103 50.8 0.10C 176 3Ü.0 t 38.0 0.130 190 38.0 0.';.87 151 38.0 0.122 192 38.0 0.18C 193 * 38.0 0.161

I> i

TABLE 6

A- 6

SUKI'LMIY OF DROP TOUTT. TiBTTf) V

RUN NO.

128

130

120

125

107

1C9

13.0

124

123

122

121

120

113

112

129

114

115

116

117

118

119

131

134

BLOW

3y.6

40.5

52.8

79.2

118.8

NO. OP

316.8

C

5

2

7

3

1

2

3

1

2

1

3

1

2

4

1

1

2

1

I

1

1

1

1

OTAL BLOW Wf.iciri' o?

ROL'K PT 0^ )

310.8 1.75 237.0 1.2S 79.2 O.ß

316.8 0.5 138.0 0.6 18.5 1.0 97.0 2.0

184.8 1.2rj 79.2 1.40

214.2 1.50 79.2 0.8

79.2 0.8

79.2 1.'25 158.4 2,25 316.8 1.0 79.2 0.6

118.8 1.2 237.6 0.7 118.8 2.0 118.8 1.0 11C.8 1.2 118.8 1.0 316.8 1.25 316.8 1.5

5»

TAhLE 6

80MMARY OF DROP TCW "• TEfTS V.i

VrtUCHT 01 niO'.: KO. OP TOT.M. BLOW V.OCK

wm NO. BHRiyj*/ BLOWS E*7SPCiY RCMO'.TD

95 145.5 1 145.5 6.0 83 2 194.0* 7.25 82 2 194.0 6.0 79 2 154.0 11.0 86 J 339.5 9.3 85 3 339.5 8.25 80 2 194.0 8.5 81 194.0 194.0 6.7 = 78 194.0 6.5 76 194.0 6.5 75 194.0 8.0 74 194.0 8.5 87 242.0 6.25 77 194.0 6.5 88 238.0 238.0 4.5 89 238.0 8.5 90 238.0 10.0 91 238.0 10.0 92 238.0 10.0 93 238.0 9.0 94 238.0 10.0 73 238.0 7.0

* Multiple blows: each blow of the set of blows is i.ot necessarily of equal magnitude.

5^

I.- ■

A) »PEN DI >: B

A shci ro:ii)».t-.-r |.;.-, r; in wnu \vrii...n !«• tlcl«.i mine

avcr.-'.j.'.cs, moan», »tAmUiirct cloviationn of Un quantitic: b,, b,,

b, b, and u.> uaint» the weighing functioui rhscii'jfd in Ilic text.

The output fu'.-.i lists i \\ the meeAured v.Juor of b.,

b^, h, and v/ciglit of : t«ck romovrd d\: it;}' each tusl with tlu-

puintcd and Wttdge-sb^ped Indcntorc ai.d then Oion-s t).«; slati-'.ice

--i.e., nvciaytu, i.vij?, i*:id »tandfrd deviation» in «aeh

variable. Interpret ] J a« bJ4 BZ at U^. 11 as h in the

pi intojt. The 95% confidence llir;*.'-. iuiply that one ha»

p 957> confidence that ihe trm: avprag« of th'- global

sömpling will fall within UMSO limit» obtained from the

csperimentc«! dat«. Tlioai* limitH ." ri^ not shown in tli<

attached printout but were calculated and used in pre-

paring F. urcs 12 and 16 in tbc text (plots of b and h

vs a).

57

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WC iK..- DH ANAf rsiS- i Uif *Q DfGRCE WLRGE

l<^l^, NO, 1 1 '.i'M- .' i 1 n • M ROCK - >■> • r.i ■ . IN. IN. rw. IM. li-

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vtlr-rl VCLL'.C

OHTCO AVERACC .^0 J'.IPS 2.|?/| |.)2r. ».f.:43 .?13 2.?^ OhlF.f) • t-'M .Bn I-.H? 2.107 l,18A |.6< ,;'.^- \f)ARf) {«f VJATIOM ,'.0 «ASA ,0^M .f«.', ,0V*i .02/i

rjHico Aveiuee 1.00 3.jv9 3,2^1 2,2AS 3.»r« i»i^: 12,'.-w GHTEO MEAN LOfi 3.;' I 3.32/i t.2FS 3.2?7 I.2/4 KOAKO DEVIATION J.öO .u'Jb .Obi .0ii9 ♦!/.« .O'."»

(iHTEO AVE^Ar.E 2.00 6.^05 6.612 5,7t9 6.6n2 e.HUV 91.917 ^rtTCO v.Ztti ?,,C0 7.011 6.7.".'* »;,cr^ 6.704 9,1CH ^DARO DCVIATION 2.00 .209 ,252 ,233 ,075 «415

frl

c. 1

NON-ispTRopic m nwro^

\\c ]\nvo ignored in l'.-'* oarlitsr analysis any anisotropy present in

the roc!;. The an.nlyiu-ä) prciblom*:vh«niunlftotropy ia incliulcd bucom«*

coi.iplicat'jd, and on the •scperimunt*] tidei ih" aumbez of testa required lo

obfcvin PtatiatlcftUy meftalnfful data becomes aatronomlcal«

A •impllfyios aaaiunption c-i?» bo introduced in that the elattlc

propertiea (E and v) can be assumed to bo isoiropic. This aaeumpttoUf

a)though it c«nno'. be defended too viroreusly, lei» one ure the available

•oKUon !r< yield some eetbnatc of vo)urru ri'.rioved .;.jd critical energiri

required to 'ritiate the fracture« Let ua further aaaume tliat the eleatie

axes art parallel to the adgea of Bio block. lin.ill« , in view of the layered

nntcre. of granite* u-t can assume strength pruperlies in directions 1 and

2 (sec Fipurc C -1) to be the FüICIC. Thu"-,

H t2 13

where rubscripts 1, 2, and 3 represent the directions shown in Figure

A total of six edge fracture combinations are poariblc as shown in

Table ^-1. Of these six (refer to Fig. C -1), numbers 1 and 3 (now Ubcled

Mode M-l) are identical, numbers 2 and 4 (labeled M-2) are identical, and

numbers 5 and 6 (M-3) are identical.

Now, as before, when o * ?» • lhc fracture initiates. Thus, in genera: xmax h there will be three different critical energies but since o is the same in

two of the directions, two of the energies will be identical. Let us use

subscript "i" to designate these energy levels as follows:

E en

2 i o, a .1

e Wagner & Brown. "Layered Igneou» Rocks." Freeman & Co. (San Francisco, 1967). s.

c-/:

./

/' " ' /./-/ AföCj£ />-%•

^'

\

/I

/- c

. • ^

• —*- ^

MOSf /f'3

Figure C_ij Face, Edge «nd Fracture Mode Designation

bf

C-i

tool normal /fmcturlng to sun'oci/iiiio surraco

Node

1 A-n :• M-l

2 S-A M-2

3 A-C H-1

4 C-A M-2

5 B-C K-3

6 C-B M-J

TABLE C-I

FRACTUkE MODES

Example: A-B means lool is normal to the face A, and

the breakout is to the face D as illustrated by M-l in

Figure C-l.

^

tLs (

The fracturi* ivo •■ ■ ? «;• ■ .. ;, .1 I>, ihc iHotrn^ic CMbr liy b

and h. Nov i-.i.-«- t. . ..i. i of i- tmd la arc p;» . i >!u.

h. ; b. - Ii, i. for Mo<!.. M i in J'..>>U C-I.

AJrto, the volume« JT»- giv< . by

i = 1 lo 3 according to Mode number M- 1 to M 3, Plate C-1 clearly

hhov.r the lhr«c di!;timt volumet consigrtud to UM? three modes. Thu-,

tin re oidercnt volumcu should «Ino b« expected. In uplte of the tcbt ».»

teat variation In rock, such di«tJnction in the volumo« v .-s indocd ohc« rved. When fr.Trtur«.- occurt. in Mod«-.b M-I end Ki-3, ono u'wu o. s: •:

* ll i'nd for M-2, wtv • = ft . Thus, lh<; fracture enorg/ for Mode 2 is l.-rper

ii:«in !).»! for Mode» M-l and ?vl-3. Since b Pnd b depend on peak l< .vds

and tetisUc, atrangtha, three distinct fre'cturc volume» v. ill, in genera), be

oLscrvod, PlateC.-l bhovs typical frnctur»'ß.

Fn practice the aUgninent between geometric and elautic axeE is

difficult to achieve, although the n.ining and rutting operation» tend to pro-,

durc «o/nc alignment. The effect» of mis-alignment can be reduced some-

what by »elective averaging technique. On Kigure C-2 we »how the experi-

mental data from T.iblc 3, Appendix A. It is estimated that in two of the

direction? the critical energy is of the order of 95 f« lb while in the ;hird

direction it may be as high as 238 ft lb. In breaking out at a single blow at the

lower energy the rock volume is »mailer than that when breaking out at higher

blow energy. Thus in one of the direction» the critical energy is hij.er

and the breakout volume is larger while in the other two directions critical

energy is smaller and there are two different volumes that breakout at this

level. The available data seems to be consistent with the above concepts.

However, the total number of tests is too small to allow any positive (or

negative) conclusions.

M

ö-^

T~-~ >•

*\ ■

....

Plate C-l: Typical three-mode fractures

C-7

/

;■■

i ■•

> 5

•

(■

:-..

0

1«

K ■

\

* m

v

:«

0) \/

'/

• ■

■ ■

^tExperimental DJa

V-E Characterifctics for OrLhotiopic Rock

pno Energy in ft /6s.

*asi / cj jf/i/% JS*SiS% »T> Siss. %

in - DTIC · subsurface fracture produced by impact in rock. 2. Reproducible and controlled...

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Transcript of in - DTIC · subsurface fracture produced by impact in rock. 2. Reproducible and controlled...