DASA 2698 July 1971 UNCLASSIFIED TRIAXIAL TESTS ON LARGE ... · Principal Investigator and Madan M....

00 CO a

DASA 2698 July 1971

UNCLASSIFIED

TRIAXIAL TESTS ON LARGE ROCK SPECIMENS

by

Peter Jay Huck

Madan M. Singh

for

HEADQUARTERS Defense Atomic Support Agency

Washington» D.C. 20305 'r-

IIT RESEARCH INSTITUTE Technology Center

Chicago, Illinois 60616

SfP 8 t97t

Contract No. DASA01-69-C-0134

■

■

■

"Approved for Public Release; Distribution Unlimited"

, 5 ', .V *■ NATIONAL TECHNICAL INFORMATION SERVICE

UrinHMd. V». MIS1

■ -

BEST AVAILABLE COPY

unciassmea 3«-:r.v C'.i^«-.'';: •••.'-! w^

1 DCCUMsNT CONTROL DATA- R i 0 ■»*'

Unclassified ill Research Institute, Chicago, Illinois ^ »"^

It. «tPOWT TITLE

TRIAXIAL TESTS ON LARGE ROCK SPECI>ENS

4. OtlC«t»Tive KOJtt Tvp* ol upon ami inclutii» i»t*t)

Draft Final Report No. D605''-23 S- AUTHOR.*'frirtr r<n«, T.IMI» inmtl. IM»I narr»)

Peter J. Huck and Madan M. Singh

«. noo«T a* TC

April 1971 T«, TOTAL S3. O* PASEt 76. NO. of men

165 45 »*. OXISINATSa'S RE»0»T NUMSEKISI

DASA 2698

DASA-01-69-C-0134 b. rnojtcT HO

AREA Order Number 1397

Progr.au. Code 9F10 »A. OTHC« nevanr NOISI (Any oth»t numt>»rt thai may d« mttiinfi

thl* np»tt)

IS. OiSTAiauTiON »-»rävcNT

Approved for public release, distribution unlimited

It. S*ONSOaiN6 MIUITAMV ACTIVITV

Director, Advanced Research Project Agency, 1400 Wilson Blvd., Arlingt< Virginia 22209

f A A studv was conducted to determine the effect of specimen size

on the mechanical response of rock. Specimens of Cedar City tonalite (Cedar City, Utah) and Charcoal Black granite (Cold Springs, Minnesota ranging in size from 2 in. dta. to 32 in. dta. (24 in. dia. for the tonalite) were tested in triaxial compression. In addition to the standard triaxial test stress trajectory, one specimen of each rock type was loaded unt^xial strain to simulate true one-dimensional compression. Test data Included axial and circumferential strain at up to 30 locations on the largest specimens, surface wires to indicate crack propagation on the 12 inch and larger specimens, axial and radial stresses and the confining pressure media temperature. Data were recorded under loading, unloading and reloading conditions. The test data for each specimen size and rock type were fit to a non-linea hysteretic model to determine variation In the model parameters as a function of specimen size. / .

ac

K C • tiOAOi

Large Triaxi-il Tests

Scale Effect;

Cedar Ci.cy Tonal Lee

Charcoal alack Grinice

Non-Linear Hyscerecic Model

■»JL-;! IT ^3i.3 «■ | o L ? 1 A'

I

IIT RESEARCH INSTITUTE Technology Center


Details of Illustrations tn^s this document may be better

studied on microfiche

IITRI Project No. D6051 Final Report No. D6051-23

Contract No. DASA-01-69-C-0134


by

Peter Jay Huck Madan M. Singh

for

Department of Defense Advanced Research Projects Agency

Washington, D.C.

July 1971

The views and conclusions contained In this document are those of the authors and should not be Interpreted as necessarily representing the official policies, either expressed or Implied, of the Advanced Research Projects Agency or the U. S. Government.

DASA 2698


by

Peter Jay Huck

Madan M. Singh

IIT Research Institute

Technology Center


ARPA Order Number ARPA 1397 Program Code Number 9F10 Name of Contractor IIT Research Institute Effective Date of Contract 15 May 1969 Contract Expiration Date 15 Aug 1971 Amount of Contract $ $99,000 Contract Number DASA01-69-C-0134 Principal Investigator and Madan M. Singh

Phone Number AC312/225-9630 Ext. 4784 Project Scientist or Engineer Peter J. Huck

and Phone Number AC312/225-9630 Ext. 4735 Short Title of Work Triaxial Tests Large Rock Specimens

Sponsored by

Advanced Research Projects Agency

ARPA Order No. 1397

The views and conclusions contained in this document are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied, of the Advanced Research Projects Agency or the U.S. Government.

"Approved for public release; distribution unlimited"

FOREWORD

This is a final report on IIT Research Institute (IITRI)

Project D6051 (IITRI Report No. D6051-23) entitled, "Triaxial

Tests on Large Rock Specimens". This research was supported

by the Advanced Research Projects Agency of the Department

of Defense and was monitored by Mr. Clifton McFarland under

Contract No. DASA 01-69-C-0134.

The project was conducted under the supervision of

Dr. Madan M. Singh, who served as program manager. Mr. Peter

J. Huck was project engineer. Other IITRI staff members who

contributed to the overall research effort include Dr. R. H.

Cornish and Messrs. F. W. Dew, L. A. Finlayson, P. A. Hettich,

S. Martin, R. D. Nelson and J. J. Vosatka.

Respectfully submitted,

IIT Research Institute

/ 4 Py y^L^l Peter Jay Huck Project Engineer

APPROVED:

R. H. Cornish Director Mechanics of Materials Division

PJHrbk

III RESEARCH INSTITUTE

TABLE OF CONTENTS

Section Page

1 INTRODUCTION 2

2 PREVIOUS STUDIES ^

2.1 Effect of Size 4

2.2 Effect of Confinement 7

3 EXPERIMENTAL APPARATUS 9

3.1 Small Test Cells 11

3.2 48-Inch Test Cell 11

3.3 Specimen Preparation 17

3.4 Instrumentation and Data Reduction 18

4 EXPERIMENTAL PROGRAM 21

5 DISCUSSION OF RESULTS 30

5.1 Theoretical Considerations for 30

Constitutive Equations

5.1.1 Formulation of Constitutive 30

Equations

5.1.2 Limit Surface 31

5.1.3 Elastic Equations 33

5.2 Typical Behavior of Rock 34

5.2.1 Hydrostatic Behavior 34

5.2.2 Triaxial Compression 39

5.2.3 Uniaxial Strain 43

5.2.4 Poisson's Ratio and Young's 43

Modulus

5.2.5 Yield and Fracture Criteria 45

5.3 Analysis of Experimental Results 47

5.3.1 Charcoal Black Granite 47

5.3.2 Cedar City Tonalite 59

5.3.3 Uniaxial Strain Tests 66

5.4 Strength Properties 72

6 SUMMARY AND CONCLUSIONS 74

IIT RESEARCH INSTITUTE

ii

TABLE OF CONTENTS (Cont'd.)

Section Page

REFERENCES 78

APPENDIX A - COMPUTER PLOTS OF TEST DATA A-l


111

LIST OF FIGURES

Figure Page

1 Typical Triaxlal Cell Schematic 10

2 Schematic of System for 2 in., 4 in., and 12 12 in. Triaxial Specimens

3 48 in. dia. Cell with 32 in. dia. Specimen 13 Being Loaded

4 Schematic of 48 in. dia, Triaxial Cell 14

3 Radial Strain Gages for Uniaxial Strain Tests 16

6 Typical Gage Layout 15

7 Loading Specimen Into 48 in. dia. Triaxial 23 Cell

8 Inserting Sliding Piston Into 48 in. dia. 24 Triaxial Cell

9 Removing Fractured Specimen From 48 in. 25 dia. Triaxial Cell

10 32 in. dia. Charcoal Black Granite Specimen 26 After Tests 27-28 (oc - 5000 psi)

11 32 in. dia. Charcoal Black Granite Specimen 27 After Tests 29-30 (ac - 10,000 psi)

12 32 in. dia. Charcoal Black Granite Specimen 28 After Test 31 (uniaxial strain)

13 22 in. dia. Cedar City Tonalite Specimen 29 After Test 32 (uniaxial strain)

14 Yield Surface for Mises' Yield Criterion 32

15 Typical Compressibility Curve for Rock, 35 After Paulding (40)

16 Compressibility of Granite, Gabbros and 36 Diabases, After Clark (41)

17 Stress Strain Curve for Nonlinear Hysteretic 38 Model


iv

LIST OF FIGURES (Cont'd.)

Figure Page

18 Idealized Stress Strain Behavior of Rock 41 After Swanson (21)

i

19 Variation of Shear Modulus with Mean Stress 42

20 Yield Criteria 46

21 Mean Stress vs. Volumetric Strain, Typical 48 Response for Charcoal Black Granite

22 Bulk Modulus vs. Mean Stress - 2" 0 and 4" 0 49 CBG

23 Bulk Modulus vs. Mean Stress - 12" 0 and 32" 0 50 CBG

24 Devlator Stress vs. Strain, Charcoal Blick 54 Granite

25 Tangent Moduli for Charcoal Black Granite, 55 2-In. Dla.



J


29 Polsson's Ratio vs. Mean Stress for 2" 0 61 and 4" 0 Charcoal Black Granite

30 Polsson's Ratio vs. Mean Stress for 12" 0 62 Charcoal Black Granite

i

31 Polsson's Ratio vs. Mean Stress for 32" 0 62 Charcoal Black Granite

32 Bulk Modulus for 2" Cedar City Tonailte 63

IIT RESEARCH INSTITUTE < !

V

Figure

33

34

LIST OF FIGURES (Cont'd.)

Page

Bulk Modulus for 4" Cedar City Tonalite 63

Variation of Bulk Modulus for Cedar City 64 Tonalite, 2-in., 4-in. and 12-in. dia.

35 Volumetric Strain for Cedar City Tonalite 64 Models

36 Bulk Modulus for Cedar City Tonalite Models 65

37 Tangent Moduli for Cedar City Tonalite 67

38 Poisson's Ratio for Cedar City Tonalite 68

39 Uniaxial Strain Test 70

40 Shear Behavior for Uniaxial Strain Tests 71

41 Volumetric Strain for Uniaxial Test 71

42 Maximum Value of VjJ" Reached for All 'rests 73

NT RESEARCH INSTITUTE

vi

i in in r'iiijimtmaronmiuimwnnrinv'ir-

ABSTRACT

A study was conducted to determine the effect of

specimen size on the mechanical response of rock« Specimens

of Cedar City tonalite (Cedar City, Utah) and Charcoal Black

granite (Cold Springs, Minnesota) ranging in size from 2 in,

dia. to 32 in. dia. (22 in. dia. for the tonalite) were tested

in triaxial compression. In addition to the standard triaxial

test stress trajectory, one specimen of each rock type was

loaded under uniaxial strain to simulate true one-dimensional

compression. Test data included axial and circumferential

strain at up to 30 locations on the largest specimens, surface

wires to indicate crack propagation on the 12 inch and larger

specimens, axial and radial stresses and the confining pressure

media temperature. Data were recorded under loading, unloading

and reloading conditions. The test data for each specimen

size and rock type were fit to a non-linear hysteretic model

to determine variation in the model parameters as a function

of specimen size.

IIT RESEARCH INSTITUTS

1


1. INTRODUCTION

Currently a number of structures are being located 1 2 underground, many of which are in rock. It is anticipated *

that the number of such underground structures will increase

enormously in the next two decades. It may be concluded that

the number of structures in rock will increase correspondingly.

In spite of this anticipated underground construction activity,

little is known about the mass behavior of rock. It is

qualitatively recognized, of course, that the rock mass behaves

distinctly differently from the matrix in small samples, but

this effect of size is not well understood, and cannot be

predicted, to date, with any degree of confidence. These

variations are attributed to joints and other weakness planes

in the rock mass. Yet, most of the test procedures for

determining strength and elastic moduli information about

rocks are based on these properties on small samples .

It is both difficult and expensive to try to perform properties

tests on larger specimens. Hence some relationships between

the various sizes need to be established. It was the intent

of this program, to study the mechanical behavior of rock

specimens of different sizes, and to determine how these

relate to each other.

During this program, two varieties of rock. Charcoal

Black granite from Cold Springs, Minnesota and Cedar City

tonalite from Cedar City, Utah, were investigated. Four

sizes of rock cores, 2-in. dia., 4-in. dia. 12-in. dia.,

and 32-in. dia. (22-in. in case of the tonalite) were subjected

to triaxial compression tests. The specimens were strain

gaged to determine the elastic moduli!. One test, on the

large core samples of each rock type was uniaxial strain

only. The data obtained was correlated to ascertain trends.


Accumulation of sufficient data on size effects

with various rock types may be expected to finally lead

to predictive equations for the rock mass. It should be

borne In mind, however, that the strength properties of smaller

rock samples are governed by mlcroflaws such as crystal

lattice disturbances, grain boundaries, minute voids (pores)

and weak cementing material. The strength of the rock mass

Is dependent on macroflaws, I.e. failure planes, joints,

cavities, and Intrusions. It also appears probable that

the rock mass Is more affected by environmental conditions

than the matrix. In general, environmental factors Induce

a time-dependent reduction In strength by chemical alteration,

rheologlcal deformation, and structural failure. The roles

of residual stresses In the rock matrix and erogenic forces

on the mass are not well understood; hence their effect on

rock, behavior requires further study. The presence of water

significantly affects the behavior of the rock mass as well

as the matrix. In general It tends to reduce the structural

strength, but whether the manner In which this Is accomplished

In the two cases Is the same, has not been clearly established.

Finally, It should be mentioned that the configuration of

the rock mass, and the base material on which It rests probably

controls Its gross behavior. It would be difficult to simulate

these conditions In laboratory samples, but the overall effects

maybe estimated by varying size and end conditions.


3

2, PREVIOUS STUDIES

2.1 Effect of Size

Several studies have been conducted to determine the

effect of size of specimens. Most of these have been with

unconflned compresslve tests. Rice and Enzian showed that

the compresslve strength of 2 1/2 - 4 In. coal cubes was about

2500 psl, whereas a 54 In. cube of the same coal failed at o

300 psl. Greenwald, Howard, and Hartmann related the size

of coal pillars to their compresslve strength at an experimental

face by over-cutting and side-cutting. There was a decrease

In strength with increasing pillar height relative to the

cross-sectional area, the breaking stress o for small pillars

approximately satisfying the relationship

,bv0.5 aco< (*) ,

where b is the lateral dimension of the pillar and h is its

height. Burton and Phillips9 studied the relationship between

size and compresslve strength of cubes of anthracite over the

range 1/4 in. to 4 in. and found that

a Pc a-0.45+0,05 c »

where a is the linear dimension of the cubes. Millard, Newman 10

and Phillips extended the range of these observations, and

used Griffith's theory of crack propagation to explain the

failure phenomenon. Both these investigations by Phillips and

his associates may be said to show that approximately

oc<* a"0'5,

Evans and Pomeroy 1 found that the relation between the mean

crushing load (9) and the side of the cube (a) Is'of the


4

form <poc aß,

where ß - constant varies between 1.5 and 2, I.e.,

-0.5 to 0 a oc a c

Holland12 has suggested a coal pillar design formula as

follows: ka0'5

where a - least width of pillar (Inches)» h - thickness of

pillars (Inches), and k - coefficient depending on type

of coal. This Is valid for a/h ratios between 1 and 10.

For rocks, the types of relationships developed are

slightly different. According to the Welbull theory ,

(f )" - CS) m v

where o - tensile or compressIve strength of the rock from a

standard laboratory test,

ü ■ equivalent strength of the rock mass,

v - volume of the rock mass,

v « volume of the test sample, and

00 - constant (with values near 10 for rocks).

The relation established by Protodyakonov was of the type

2». i + «(*- 1) am 8 + *

where s - spacing between major discontinuities In the rock

mass, e.g., joints, beds,

a - dimension of the test specimen, usually diameter

for compression tests, and

IIT RISCARCH INSTITUTE

K - mass fracture coefficient (in compression:1-2 for

igneous rocks, 1-3 for competent sedimentary

rocks, 3-iO for weak rocks; in tension: approximately

double these values).

Grobbelaar , based on the work of Epstein , Bieniawski ,

and others, found that the formulae relating the modal

strength of the weakest elements and its standard deviation,

based on the weakest link theory, are

oN - au - o8 (21ogN)0'5- 1/2 [log(logN) + log(4 )} (21ogN)"0-5

and a (N) - oa xir(121ogN)'0,5

8 8

or as(N) - as(N0) (logN0/logN)0-5

where N - number of flaws in the large cubic specimen,

■ number of unit cube.

N - number of flaws in the small cubic specimen or

Oj, - modal strength of the weakest link in a sample

containing N elements,

a - average strength of a unit cube of material

containing N elements.

og - standard deviation of the modal strength of

samples containing N elements,

and 08(N) - standard deviation of the modal strength

of the weakest element in a sample containing

N elements.

These formulae are based on the "weakest link theory",

which can be analyzed mathematically if it is assumed that

the frequency of occurrence of events is a continuous

function (e.g. Weibull13 or normal distribution). The "links"

in this case are the macroflaws (or cracks) in the bulk

material; not the microflaws.


6

18 19 Glücklich and Cohen » have indicated that effects

other than statistical exist, since the total stored elastic

energy increases with specimen volume. The energy released

at onset of fracture is related to initiate fracture; in other

words, this reduces the rock strength. This phenomenon has

been recently discussed by Baecher .

2.2 Effect of Confinement

There have been numerous studies investigating the

effects of various aspects of confinement on rocks. It is

not intended to review all of these completely in this section.

Most of the pertinent work has been briefly discussed by 21 Swanson , The earliest experimental work was performed by

22 23 Adams and von Karman . However, significant headway was

24 not made until the initiation of work by Griggs and

2*1-26 his coworkers . Since then a number of

researchers have conducted various types of studies under

pressure several of which were presented at a symposium on

rock deformation . Baidyuk has summarized some of the

Russian and American work. Research in this area is still 21 29 30

very active * * . All of this work has been performed

with small rock specimens, a few inches in diameter. As a

result considerable light has been shed on the behavior of

the rock matrix and the criteria of failure. Refinements

to the Griffith hypothesis have been proposed 33 and

appear to explain the rock fracture process under confinement

fairly well. The extrapolation of these theories to larger

rock masses is of doubtful value and hence large scale

field testing has to be resorted to . The U. S. Bureau of

Mines has undertaken a rather comprehensive program to

collect field data with the intention of correlating it into

a hypothesis 5. The contributions of Hoek36, Bieniawskl37.

Cook , Wawersik-'0 and Houpert"" to the mechanism of brittle

failure in rock deserve to be noted even though the studies

lir RESEARCH INSTITUTE

were not conducted under a confined state of stress.

To the best of the authors' knowledge no experimental

Investigations on large rock samples under confinement have been performed.

IIT RCSEAICH INSTITUTE

8

3. EXPERIMENTAL APPARATUS

In order to conduct triaxlal tests for the range of

specimen sizes used on this project, four triaxial cells

were set up as shown below:

Chamber I.D. (in.)

Specimen Diameter (in.)

Maximum Chamber Pressure

(ksi)

Maximum Axial Load lb. x 10°

4.0 2.06 30 0.375

6.5 3.65 30 0.990

14.7 10-12 20 3.40

48.3 22-32 20 axial 10 confining

36.5

In a standard triaxial cell the axial load is supplied by an

external loading machine. However, in order to achieve the

large end loads required for the tests in this program, these

chambers were separated into two regions by sliding pistons.

The general configuration is shown in Fig. 1. One region

contained the specimen, and was pressurized to the desired

confining pressure. Axial load was transmitted to the rock

by the sliding piston. The maximum axial stress in the rock

depends upon the ratio of the rock and piston areas and the

difference in the confining pressure and the axial chamber

pressure. The specimen stresses are given by the following

equations:

where

a2 - 03 - P3

Affl " <VP3> Xf al - ^3 + Aal

A • piston area

Ar - specimen area

MT RtSEARCH INSTITUT!

9

Chamber Closure with Instrumentation Lead- Out

Confining Pressure Region

Test Specimen

Sliding Piston with Loading Blocks

Axial Pressure Region

Fig. 1 TYPICAL TRIAXIAL CELL SCHEMATIC

10

P* * axial chamber pressure

Fo ■■confining chamber pressure

Acr, - deiviator stress

a-, a« and ö- "principal stresses.

Reference to Figure 1 and the above equations confirms that ' if P, ■ F~, Atfj « 0 and the specimen is uhder hydrostatic stress (<J, " a2 m a^' ôr P3 " ®* t:ê 8Pec:^men ^8 unconfined, with eg - a3 - 0 and ^ - AO^ - V^ A /Ar. ' '

3.1 Small Test Cells i

The three smaller test cells are Incorporated into a testing system with centralized controls, instrumentation, and pumping systems. A schematic of this system is shown in Fig. 2. The tests conducted in this system consisted of initial hydrostatic loading up to the desiredj conflnlhg pressure, followed by triaxial compression at constant p* above that pressure. At least one load-unload-reload cycle was observed for each test. Provision was made for pressure cross-connections between the'confining pressure and axial pressure chamber volumes to Insure hydrostatic conditions during the hydrostatic test phases.

3.2 48Înch Test Cell ) ■ ^ — ■ i •

This test cell is shown in Figs. 3 aiid 4. The basic unit is a 48" I.D. by 86" working length,chamber having ' 20,000 psi design working pressure. The chamber walls are built up from rings 12" long which are held in place by a 3/4" thick liner on the inside diameter. The entire axial load is carried by a flexible reaction frame which was built up from steel strap. The l40 ton weight of this' chamber is substantially less than the weight that would have been required by conventional chamber design. This is the

IIT RESEARCH INSTITUTE i

11

3!

»

M

CM

z M

M

CM

i CO

CO

fa o ÜCO MZ EH

WÜ

U fa COCO

CM

00 •l-l fa

12

NOT REPRODUCIBLE

Fig. 3 48 IN. DIA. CELL WITH 32 IN. DIA. SPECIMEN BEING LOADED

13

largest chamber currently available at IIT Research Institute,

and is capable of applying axial loads of 36 million pounds

to rock specimens as large as 3 1/2 ft. in diameter.

As can be seen in the schematic, the pumping

and control systems for this unit are simpler than for

the small chambers. A separate pump was used at each end

of the chamber. Accumulators were not used because the

chamber volume itself is large in comparison with other

available pressure chambers.

The operation of this chamber is similar to that

of the smaller chambers, except that the turn-around time

between tests in on the order of a week instead of an hour.

The tests in this chamber differed slightly from those in

the smaller test cells. In order to maintain seal integrity,

a positive pressure differential of about 200 psi was maintained

across the sliding piston during the "hydrostatic" portions

of the triaxial tests, and the axial pressure was not allowed

to drop below 400 psi at the bottom of the load-unload-reload

cycle. Had these precautions not been taken, there would

have been danger of upsetting the piston seal, thus aborting the remainder of the test.

TWo of the large specimens were loaded to produce

unlaxial strain. Figure 5 shows the two transducers were

designed to provide measurements of average radial strain.

One transducer consisted of a full strain gage bridge using

manganin wire elements. The active elements each consisted

of 4 turns of manganin wire wound tightly around, but not

bonded to, the specimen. Temperature and pressure compensation

were achieved by similar elements loosely wound on the

specimen next to the active elements. The second transducer

consisted of an open steel loop pinned to the specimen.

The open ends of the loop were Jointed by a flexible strap

mounting foil strain gages as shown in Figure 5b. Small


15

Active Elements

Passive Elements

5a - Manganln Wire Gages

Strain Gages on Flex Strap

Contact Points

5b Beam Type Gage

Fi8* 5 !ESTSL STRAIN

GAGES F0R UNIAXIAL STRAIN

deflections at the diametrically opposed pins cause relatively large bending strains In the flexible strap. This transducer suffered from somewhat erratic operation, as Is usual with any point-to-point gages on rock specimens.

3.3 Specimen Preparation

Specimens of the Charcoal Black Granite were bought from Cold Spring Granite Co. In Cold Spring, Minnesota, but the Cedar City tonallte was supplied by DASA. In both cases, the larger cores (10 or 12-ln. and 22 or 32-ln. dla.) were obtained as such from the source, but the 2-in. and 4-in. dla. specimens were cored In the laboratory from extra rock obtained In each case. These smaller cores were cut parallel to the axis of the larger cores so as not to Introduce complications because of anlsotropy.

End preparation of the 2-ln. and 4-in. dla. cores consisted of facing on a lathe until the ends were plane and parallel to 0.001 inches. The larger cores were capped in a specimen cage to permit handling. The capping material used was a steel-filled epoxy. Figures 3 and 7 each show an assembled 32 inch specimen in its cage. The cage tie rods were designed with end fittings that would accept tensile load only. Since the maximum tensile load that could be applied to the cage by these tie rods corresponded to 30 psi compressive stress in the rock specimen, the effect of the cage on the rock was negligible.

An array of foil strain gages were mounted on each specimen. The number used ranged from three rosettes on the 2 in. cores to thirty rosettes on the 32 in. cores. These were two element rosettes with 1/4 in. gage length placed with the direction of rolling parallel to the specimen axis. The gage placement procedure included the following steps:

* grind the rock surface

* apply two thin coats of gage cement NT RESEARCH INSTITUTE

17

* visual Inspection for voids In the cement base * affix and wire gage * apply two coats of gage cement for water proofing * check gage for continuity and response (soft

eraser) and replace If necessary.

In several cases It was necessary to move a rosette slightly away from Its pre-determined location because of local flaws or drill shot embedded in the surface (especially in the case of the tonslite).

In addition to the gages, break wires were cemented to the surface of the 12-in. and greater diameter specimens. This wire was No. 36 manganin wire well bonded to the surface so that the wire would break if a crack propagated across it during a test. Figure 6 shows typical instrumentation for a 12-in. core.

The Instrumented cores were waterproofed with latex cement over the foil gages, and at least two coats of latex paint with a thickening agent spread over the entire rock surface. Waterproofing is very important in a triaxial test since both the loading conditions and the character of the rock can be changed by intrusion of oil into the rock voids. In those tests where the specimens could not be loaded to failure on the second load cycle, the specimen was recovered intact and stripped of paint for visual inspection. In several cases, traces of oil were found under the paint, but typically the specimens were completely dry. In no case was there enough oil to do more than dampen a very small area on the specimen surface.

3.4 Instrumentation and Data Reduction

The instrumentation on this program Included foil strain gages, temperature transducers, pressure gages and break wires on the larger specimens. All instrumentation except the pressure gages were recorded using an automatic

III RISIARCH INSTITUTI

18

Axial Surface Wire

Circumferential Surface Wir<

Foil Strain Gage Rosettes In 4 x 6 Matrix

Fig. 6 TYPICAL GAGE LAYOUT

19

data acquisition system. The pressures were read using

Hiese Super Accurate bourdon gages and inserted manually

onto the data system output as they were read.

Due to the bulk of data involved, the data were

reduced and plotted using the 1108 Univac computer at IITRI.

In addition to printed output, the following plots were

produced for each test:

Shear strain vs. deviator stress

Volumetric strain vs. mean stress

Poisson's ratio vs. mean stress

Octahedral shear stress vs. mean stress

Circumferential and axial strain vs. axial

stress

Elastic, shear and bulk moduli vs. mean stress.

Data from each test was then assembled by hand to show trends

from test to test.

HT RESEARCH INSTITUTE

20

4. EXPERIMENTAL PROGRAM

The program included trlaxlal tests on specimens

ranging from 2-in. to 32-in. dia. One uniaxial stiain test

was conducted on the largest available specimen for each

rock type, these being a 32-in. dia. granite and a 22-in.

dia. tonelite. The uniaxial tests were conducted by monitoring

mean radial strain and maintaining sufficient confining pressure

to hold this strain as near zero as possible. The experiments."V

program is summarized in Table 1. IITRI was able to procure

the granite core from Cold Springs Quarry, Minnesota. The

tonalite specimens were delivered by DASA which was unable

to obtain more than one large specimen of tonalite.

The loading and unloading sequence in the large

chamber is shown by the photographs in Figs. 7, 8 and 9.

Typical failures are seen in Figs. 10 thru 13.


21

f-l X) (0 H

<

I H OL W

X w

H

r-l \ / \ / \ / \ 1 Iw v 1 CD C \ / \ / \ / \ 1 \ / \ / •rl*H \ / \ / \ / \ 1 \ / \ / X CD \/ \/ \ / H \l \/ \ / «N CD U v v v CO Y Y Y CO

■M 4J X X x A A \

lM A A A A A A >H i w \/ CO

\ / \ / CO \ / \/ CM \ / \ / Ü •4- ON y x CO

CO <M y y 0 m A A CM /\ i\

o H /\ /\ / \ I \ 0) / \ / \ / \ / \ Vi / \ f \ / \ / \ 3 f '. f \ 10 y / (0 \ / 0) •H o \ / M so CO \ / S * <t ^ o 1 *o 00 00 \j

<-4 l-< H ON CM l-l CO i Y M) a M f\ Ö M I \ i-l / \ C1 / \

C / ' \ \ / 0 « \ /

Ü ^H r-l 00 m sO \ / « fM <M «M CO v J* ^ ON •|>. 1 « 9k r*. x

T-l von r* ^i- m H A »n H <N «N' CO /\

1 /, \

<u •

i

.

; 1

h 5 <NJ <t <N CM fS St <N CM 0»^ H co j H CM UQ /

l-l CD «

i I O 4J ' »J '

Rock

Type

Chare

Black

Grant

i Cedar

City

Tona

l:

22

NOT REPRODUCIBLE

Fig. 7 LOADING SPECIMEN INTO 48rINJ DIA. TRIAXIAL CELL

NOT REPRODUCIBLE

Fi8' 8 Tmx™GCELLDING PIST0N INT0 48-IN- DIA-

24

NOT REPRODUClBLE

Fig. 9 REMOVING FRACTURED SPECIMEN FROM 48-IN. DIA. TRIAXIAL CELL

25

NOT REPRODUCIBLE

Flg. 10 32-IN. DIA. CHARCOAL BLACK GRANITE SPECIMEN AFTER TESTS 27-28 (ac - 5000 psi)

26

NOT REPRODUCIBLE

Fig. 11 32-IN. DIA. CHARCOAL BLACK GRANITE SPECIMEN AFTER TESTS 29-30 (ae - 10,000 psi)

27

NOT REPRODUCIBLE

Fig. 12 32-IN. DIA. CHARCOAL BLACK GRANITE SPECIMEN AFTER TEST 31 (UNIAXIAL STRAIN)

NOT REPRODUCIBLE

Flg. 13 22-IN. DIA. CEDAR CITY TONALITE SPECIMEN AFTER TEST 32 (UNIAXIAL STRAIN)

29

5. DISCUSSION OF RESULTS

5,1 Theoretical Considerations for Constitutive Equations

The large amount of data generated during this program

makes a simple report of experimental data inappropriate.

The reduced data itself consists of an 8 1/2 inch thick stack

of printed computer output. Since it was obvious at the

start of the program that this would be the case, parallel

computer output in the form of graphical plots was provided

for inclusion in the report as an appendix. In order to

summarize the data for discussion in the text of the report,

it was felt that the most convenient form would be a comparison

of the test data with a model. The model parameters can

eben be evaluated as a function of specimen size much more

easily than the actual data.

5.1.1 Formulation of Constitutive Equations

Concepts from the theory of plasticity have recently

been used to describe the behavior of particulate materials

such as soil and rock. If a stress space is constructed with

coordinate axes representing the three principal stresses,

the state of stress of an element of material is described by

a point in this stress space. The locus of all possible stress

states which cause yielding of the material is a surface called

the yield or limit surface. This surface separates the

stress states attainable in the material from those which are

not attainable. An elastic-plastic material is one which

behaves as an elastic material at stress states within the

limit surface, and as a plastic material at stress states on

the limit surface. A material model thus must Include both

a description of the limit surface and the elastic equations

that hold within the limit surface.


30

5.1.2 Limit Surface

The limit surface in principal stress space is usually

expressed by

iJf - f(Jj.) (i) In which J, is the first invariant of tbi stress tensor and

JX is the second invariant of the deviatoric stress tensor. These invariants are defined by

Ji (a^a^2 + (al - a2)2 + (a2 - a3)

2

(2)

(3)

in which o-,, ar^i and a- are the three principal stresses. An

equivalent method of describing the yield surface is to write the octahedral shear stress, T tj as a function of the octahedral

normal stress, ou«*-» or

in which

and

W - f(aoct)

ffoct - T <al + a2 + ö3>

koct 1 7 (ol-a2)2 + (a1-a3>

2 + (a2-a3)2

(4)

(5)

1/2 (6)

One form of a yield surface commonly used is the

Mises1 yield criteria given by

J2 - Ko (7)

in which K0 is the yield limit of the material in simple shear.

Equation (7) describes the surface of a cylinder in principal

stress space with the axis inclined equally to all three

principal stress axes as shown in Fig. 14. According to Mises*

yield criterion the shear strength of a material is independent


31

Radius V2 K.

Total Stress Vector Vector /-v

Axis of Yield Cylinder

(0! - o2 - 03)

Fig. 14 YIELD SURFACE FOR MISES' YIELD CRITERION

32

of the mean stress a , where

In granular materials, Including most soils and rocks, It

has been established that shear strength Increases with

mean stress due to frlctlonal behavior. For these materials

the Coulomb-Mohr yield surface Is more applicable, and Is given

by

VJ]~ - A + B JJ^ (9)

In which A and B are constants. Equation (9) describes the

surface of a cone In principal stress space with the same

axis as the Mlses1 yield criteria shown In Fig. 14.

5.1.3 Elastic Equations

Constitutive equations for an Isotropie linear elastic

material are given by

alj ■ ^ljekk + 2^lj <10>

In which a^. - stress tensor

Ejj - strain tensor

d.j - Kronecker's delta

>%>tl are Lame's constants.

It Is sometimes convenient to separate the volumscrlc response which Is produced by mean stress from the distortion«! response which Is produced by shear stress. This Is accomplished through the devlator strain tensor, e'j4» and the devlator stress tensor, a£., which are defined as

Eij ' eij " T ekk filj <U>

aij " 0lj ■ ? akk 6lj (12)


33

The constitutive equations (10) may then be rewritten In the

form , » "a m k 8ij ekk + 2G4j <13)

In which k and G are respectively the bulk modulus and shear

modulus. These moduli are defined by

- a., a- + a« + a0

o-l a»

r1 ' , (l5) e Ij

Nonlinear behavior may be Incorporated by using an Incremental

constitutive relation and defining k and G as functions of

one or more of the stress Invariants. Inelastic behavior

may be Incorporated by using separate values of k and G for

loading and unloading. The unloading moduli must be greater

than the loading moduli to prevent energy generating hystersls

loops.

5.2 Typical Behavior of Rock

5.2.1 Hydrostatic Behavior i

Past work has shown that the stress-strain behavior of rock subjected to hydrostatlq pressure Is non-linear. A

typical curve of mean stress versus volumetric strain from

Pauldiqg Is shown In Figure 15. In an unloaded state a

rock specimen usually has an Initial porosity, Including some

small cracks. As hydrostatic pressure Increases, the cracks

begin to close and the porosity decreases, causing the rock

to become stlffer and less compressible. At higher pressures

the response becomes linear and compressibility of the rock

may be predicted from the Individual compressibilities of

Its constituent minerals. The Initial porosity may be determined

by extending the linear portion of the curve back to the

strain axis. Based on data presented by Clark , shown In

Fig. 16, It appears that the Influence of the Initial

IIT RISCARCH INITITUTI i

34

I

Compressibility of Solid Material

Volumetric Strain

?ig. 15 TYPICAL COMPRESSIBILITY CURVE FOR ROqC, AFTER PAULDING

35

Granites

2Z22ZZZ222ZZ2 Gabbros & Diabases

yzzzzzzzzzzzzzzzzzn

J I I I I I \ I I I L 0 2 4 6 8 10 12

3 Pressure - Bars x 10

Fig. 16 COMPRESSIBILITY OF GRANITE, GABBROS, AND DIABASES; FROM CLARK41

36

porosity on compressibility becomes negligible at a pressure

of about 2000 bars or 29 ksi.

The behavior of granular materials under hydrostatic

pressure has been studied analytically through the use of

models consisting of various packings of elastic spheres .

Hertz's contact theory has been used and has shown that

the volumetric strain is directly proportional to mean stress

to the two-thirds power. This nonlinear!ty in response is due

to the geometry of the packing of the individual particles

and not the properties of the material comprising the spheres.

The Hertz theory may be applicable if rock may be considered

as a granular material.

A nonlinear hysteretic model used by Seaman and „44 Whitman to study the behavio..* of sand appears to be suitable

for representing the hydrostatic behavior of rock. The

stress-strain curve for this model is shown in Fig. 17. For

virgin loading

%-*! ** a«) and for unloading and reloading

V - A2 (ev ■ evi in which

° - A9 (e„ - e -)n (17)

a-. " mean stress m

e ■ volumetric strain

e». - residual volumetric strain

A-^ and A2 ■ material properties This model represents both the nonlinear and the Inelastic

behavior of the rock observed under hydrostatic loading.

Application of the mathematical model in a

computer code would perhaps be most convenient in an

incremental form using tangent values of bulk modulus,

■ IT RESEARCH INSTITUTE

37

a = A0(f. -e „ ) n

Volumetric Strain, e

Fig. 17 STRESS-STRAIN CURVE FOR NONLINEAR HYSTERETIC MODEL (after Seaman & Whitman^)

38

kt. This modulus is a function of mean stress and for a given stress represents the slope of the curve at that

stress level.

For loading

k^ ■ m ■ n A., a KLO)

and, for unloading and reloading

kt-% - n Aj/n a"-1/n (19) v

Note that in this model the modulus for unload-reload is larger than the modulus for virgin loading at any given stress level.

5.2.2 Triaxial Compression

A triaxial compression test normally consists of two phases. First, a hydrostatic confining stress, a , is applied to the specimen so that the principal stresses are all equal- to ac. Then, two principal stresses, 02 and a-, are kept constant at o while the third principal stress, a., is increased. For these conditions one of the components of the deviator stress is

ail " al " 1/3 (al + 2a3) " 2/3 <ara3> <20) If the material is Isotropie two principal strains, e^ and Ey are also equal, meaning that the corresponding component of deviator strain is

eil " el ' 1/3 (el + 2e3> - 2/3 <el " e3> (21>

Thus, for triaxial conditions the shear modulus may be determined from

21^- T^TT^ (22)

III RESEARCH INSTITUTE

39

Idealized behavior of a rock specimen loaded li> 21

triaxial compression as presented by Swanson '" Is shown

In Fig. 18. The relation between devlator stress and st/aln

Is linear up to yield. At stress states beyond yielding the

relation becomes nonlinear and plastic behavior occurs.

The modulus for unloading Is equal to that for virgin loading

to the yield point.

Volume change behavior Is the same as that for

hydrostatic loading at stress states below yield. At yield

the volume of the specimen begins to Increase even though

the mean stress Is compressIve and also Increasing. This

tendency for rock to expand when yielding Is termed dllatancy

and Is characteristic of almost all partlculate materials.

At low stress levels shear modulus Increases relatively

rapidly with mean stress; however, at higher stresses It

remains relatively constant. Torslonal wave velocities

were measured In cylinders of different granites exposed 2 2

to hydrostatic pressure between 1 kg/cm and 4,000 kg/cm

by Birch and Bancroft . From the wave velocities the modulus

of rigidity, which is identical to the shear modulus, was

determined and is shown as a function of mean stress in Fig. 19.

Also shown in Fig. 19 are values of shear moduli for specimens

of Charcoal Black granite and Cedar City tonalite determined

from triaxial tests performed during this study. The moduli

determined by Birch and Bancroft and those for the Charcoal

Black granite are in good agreement and increase approximately

with the 1/10 power of the mean stress. Values of shear

modulus for the Cedar City tonalite are, however, radically

different. At mean stress levels below about 5 ksl, the

shear modulus Increases with the 5/6 power of mean stress.

At higher stress levels, the shear modulus increases less

rapidly. One probable cause for this change in behavior

is the relatively high initial porosity of the tonalite.

MT RESEARCH INSTITUTE

40

Fracture

De via tor Strain, ^j-fo

a) Shear Stress-Strain

r-ll

CO

CO CO 0)

t CO

c

Hydros tf

Dilatancy Curve

Volumetric Strain, ej^ + e2 + e

b) Volume Behavior

Flg- 18 ^Li5lNS^S-STRAIN BEHAVI0« OF ROCK,

41

"^~" ■"^^

-

■ cn Q.

-

1 *. ^n f-4 ' OrH 1 r-l C

I X 0

c

ft

*c t^ TO

• 3

ii e 0

rt m 14 ^ f -d- JFi ^ X ^

i _i il \ i o 11 \ CM

u U \ •

r-l

i y* 11

'- 11 w '■" 11 V

| X) i j \ ! -3 41 \ _

- il \ - O 111-* \ V. > k —

•l—t i ^^^ v*^ ! r^ i ■ X ■ c 11 \ - i ^_ X. 0 ■ I V 1 u El X

i ^

-*- •H

a» 1 w 1

TO 1

O -

<—— OJ d) ^-1 o | u *J TO ^~

• -( ..-I 01 C •^ 1 r c •w 0 o 1 TO ^j •H H TO >-i ^ c i—i 1 -

| Ü o TO 4J

CO

>> 4-. c; •H r-i H rH U u TO

i VJ O >s 0 I oi a o M O ! J_I ^ c TO u 1

en u •H TJ TO I <U O 3 0) £ 1 — S OS O* O O i.

1

■

.1.

o

i i i

T -L. 1 i i i 1

o o

— o

_ o

o t

o

CO M M

CO

•r-l P2 CO H ^ M

^ M

e CO n Ö

1-1 #i D

w O cn 0) jgj ^ 4J CO

SSj

C g TO CO CU S b

o •^ o H H < H

^

«T»

bO

o

^^ « OT x TS>I <49 'sn^npow aeaqs

42

Values of shear modulus shown in Fig. 19 are tangent

values, Gt, which refer to the t^lope of the deviator stress-

strain curve at a given stress vfclue. For nonlinear behavior

the tangent shear modulus is a function of mean stress and

may be calculated from

d(o, - a,)

°t - ^ j^h^r (23)

The functional relationship with mean stress may be written

as Gt- " c a (24) t m

in which c is a constant.

5.2.3 Uniaxial Strain

The uniaxial strain test is a special type of triaxial

test in which the lateral strains, 62 and e3, are equal to

zero throughout the test. One method of obtaining this

condition is through monitoring the lateral strains and

controlling the lateral stresses, Oj and o^, to maintain

zero strain. In soil mechanics, for the uniaxial strain

loading, the ratio between the lateral and axial stress is

called the coefficient of earth pressure at rest, K , where

K - !3 . (25) öl

Data from this test may be used to compute bulk and shear

moduli from the following equations:

öI G - 1/2 ^ (1 - K0), and (26)

k = 1/3 ^ (1 + 2K0). (27)

5.2.4 Poisson's Ratio and Young's Modulus

Two constants are necessary to describe the stress-

strain behavior of an Isotropie elastic material. One set


43

of constants, k and G, which separate volumetric and

deviatoric behavior have been described previously.

Another pair of constants which are commonly used are

Foisson's ratio, v, and Young's modulus, E. The constants

E and v are derived directly from a triaxial test in which

the lateral stresses, 02 and o^, are equal to zero. For

this special test condition.

E - i, and (28) E 1

- - -* (29)

For more general test conditions

9kG E - 3k + G , and (30)

The use of tangent values of bulk and shear moduli, kt and

Gt, in equations (30) and (31) will result in tangent values

for Foisson's ratio, vt, and Young's modulus, Et.

For hydrostatic loading the deviatoric stresses and

strains are zero and G is undetermined. Therefore, E and v

are also indeterminate from a hydros tat. For a triaxial

test with a3 equal to zero, E and v may be computed from

equations (28) and (29). For a triaxial test with a~ unequal to zero but constant, tangent values of E and v may be computed from

(32)

(33)

Et - da^

, and

vt ■ •


44

For more general conditions equations (30) and (31) must be used.

For unlaxlal strain tests the following expressions oay be used _

E-^ —n-hg—-•"'* w

v- r-^g- . (35)

5.2.5 Yield and Fracture Criteria

In principal stress space the restraint a2 m a3 defines a plane which Includes the a,-axis and the axis of the yield surface shown In Fig. 14. As a« - a3 Is a condition maintained during the trlaxlal test all stress states In this test lie In the c^ - a« plane. Thus, yield and fracture criteria may be described by a curve In this plane. Curves representative of different failure criteria are shown In Fig. 20 with J^ plotted vs. V J* on orthogonal axes. The stress path for a constant o3 trlaxlal test Is also shown In Fig. 13.

A thorough discussion of yield and fracture surfaces as they apply to the behavior of rock has been given by Swanson . The yield surface defines all stress states at which the rock ceases to be an elastic material. At stress states within the yield surface some form of elasclc equations govern the material behavior. At states on the yield surface equations from plasticity govern the behavior. It has been shown that most rocks exhibit strain-hardening behavior; I.e., the Increase of stress beyond Initial yield causes the yield surface to move outward. Continued Increase of stress causing outward movement of the yield surface will eventually result In failure of the rock. The locus of all jtress states causing failure Is called the fracture


45

Pi I 3

o CM

00 •rl

46

Wm/M'mmm

surface or failure surface. <

5.3. Analysis of Ekperltnental Results

Experimental results are presented In a form

consistent with the elastic-plastic constitutive model

presented earlier. Elastic properties are presented as

functions of mean stress and are given In terms of tarigent

values which are compatible with a nonlinear incremental

form of elasticity equations. Yield and fracture criteria

are presented in the form J« " (Ji)•

5.3.1 Charcoal Black Granite

Typical volume change data from a constant confining

pressure triajcial test is shown in Fig. 21 along with a curve

representing the nonlinear hy^teretic model fitted to the ■■ experimental data. The constants for the model were conven-

lently determined from logarithmic,plots of the data, In

the middle portion of the curves experimental results and

the model are in close agreement. At relatively low stress

levels, less than 2 ksi, the model predicts, stresses that

are smaller than those measured. Fracture of this specimen

occurred at a mean stress of 17 ksi and yielding had begun

at about 14 ksi which results in dilatant behavior of the

specimen at thesö stress levels. T^ius, as would be expected

the model and experimental results dp differ at stress levels

greater than 14 ksi for this particular specimen.

Tangent values of bulk modulus, Kt, were determined

from the experimental data and plotted as a function of

mean stress in Figs. 22 and 23. These values represent

the computed slope between actual consecutive data points

rather than the slope of a smooth curve drawn through the

data points. This procedure Introduces "noise" i,n the

plots since the data points are rather close together and

the Uncertainity in the computed volumetric strain is rather

large in comparison with the change in volumetric strain over IIT RESEARCH INSTITUTE

47

. ...._ ,- ■ . - ■■ . ■ ■ ::•. :.•,.• ■■ ■■ . ■■ •■■■v BMHWiaiK^fWffaMlgByW^Ba^^ 11

18

16

14

12

10

0 n o 3

to (0 0)

co 6 c CO 0) as

Test No. 12 2 in.-dia. Specimen o.j ■ 5 ksi

Model (Load)

Aj^ - 2.1 x 10^ ksi

Model (Unload-Reloac)

v 'vi

2.6 x 105 ksi

e - 2.5 x 10"4 ve

i I 8 12 16 20 24 28

3.3 -4 Volumetric Strain, ev, in /in"' x 10

Fig. 21 MEAN STRESS VS. VOLUMETRIC STRAIN, CHARCOAL BLACK GRANITE

48

^Sj*w?PW8»W5«(l^ WiWgSwW«*^^

M

i

l-l 3

14 — —

14 o

0 Te8t. i2 2-in. dla. granite

12 - 6

D

Test 14 oo

Test 34 ^ 4 A 10

8 -

o c

oooo0o «^ n DDDDa

6 -

4

m ̂ 1 ■ A

2 Solid Symbols indicate Hydrostatic Data

_J 1 J i I l l i i i

8 10 12 14 16 18

Mean Stress, <J , ksi tn'

20 22

14 U

1'-

10

8

6

4

2

° -

4-in. dia. granite 0

oo o ^

_ 0 Test 9 o

A Test 11 0

- O Test 19

■ ■ <<

4

A ^

'*? O

Y Solid Symbols indicate Hydrostatic Data {

1 1 -J L L -J 1 ' i L.- 1 1 8 10 12 14 16 18 20 22

Mean Stress, a , ksi

Fig. 22 BULK MODULUS VS. MEAN STRESS - 2" 0 AND 4" 0 CBG

49

: ., . .. ,. ■ -■ ., ;

CO M

•> 4-1

^5

CO 3

i-i 3

•V

3 CO

•I-I CO

(O

3

3 PQ

12 p-

10 -

16

14

12

10

8

6

4

2

Test 20 o 10 ksi

" 16 A 5 ksi

12-in. dia granite

o

o

Solid Symbols Indicate Hydrostatic Data. , , i

10 12 14 16 18 20

Mean Stress, orm, ksi

0 o

[— m

4

Test 28

" 27

o 5 ksi

^ 5 ksi

t 4 ■

■ D " 29 DD n"D 30

A 10 ksi

□ 10 ksi

A > S ^ a Q 0 r '% ■ 32-in. dia granite

r / ■ t D

L/ t r * •

■ &

Solid Symbols Indicate static Data

Hydro-

1 M. _L w^m —_ J I l 1 1 L I 10 12 14 16 18 20

Mean Stress, o . ksi m

Fig. 23 BULK MODULUS VS. MEAN STRESS - 12" 0 AND 32l, 0 CBG

50

Wmsmmmmmmmmmmmm ■■v-■7^.ri;v,;1^>^-i■^..^v-,;.«:.i^;v^t■■^■:r^^'^^■■^:v;>■ ■,';■.■■ ■■..-■■; .- -,;-: ......^-,..:■ . ....

the short interval between data points. Each plot Is

superimposed on the values of bulk modulus predicted by

the nonlinear hysteretlc model for the particular core

size. Several trends are Immediately apparent. First,

the experimental data fits the model best In the hydrostatic

range of each test, and departs from the model at low

stress levels and at high stress levels where yielding la

to be expected. Second, the fit to the model Is best for

the small specimens and worse for the large specimens.

This Is probably a result of the relatively early slippage

that took place In the larger specimens. The larger specimens

began slippage at low levels of devlator stress, so that

earlier departure from the model Is to be expected. Of course.

It Is to be remembered that the model was developed for small

rock specimens.

Table 2 Is a summary of the model parameters for the

tests on Charcoal Black granite. The smaller cores behaved

quite consistently, and the model parameters were simply

averaged to produce the final parameters for each test.

The larger tests were less consistent, particularly with

respect to the values for A^. The final parameters for the

32-ln. specimens were obtained from a composite log-log

plot of data for tests 27, 28 and 30.

An Interesting comparison may be made between the

analysis of an ideal packing of elastic spheres as discussed

earlier and the observed hydrostatic behavior of the rock

specimens. Values of "nM in the nonlinear hysteretlc model

vary from 1.59 to 1.93 with an average of 1.74 for the

specimens of Charcoal Black granite. The corresponding

values of "n" for the ideal packing is 1.5. For granular

soils n values between 1.5 and 2.0 have been observed^.


51

^^^^^gmÄ^mu:^^-----,.

:- gsfp^enw ■■■ "■.-.

^> CO H

O

CO

öl H H

- o N X

•r4 4-1 (/)

C U) CO VJ (U o So c

o

OH io CO

(0 0) H

i (0

<N m o a»

oo

CO

oo m <t vO o t-t ON vt" m T-i CTN n 00 ^t O 00

• • • • eg <N

• • • o

• • <N

• • • O O O i-l rH O

I-H CNJ cn vo »n vo

vO O i-l 00 f^» 00 00 <T> vO !T> o r*

m in m o m oo o oo

mom mom

«N -d- -d- rH r-l CO

ON r-l a»

CN

m m o

vo r«. o rH «^1 cs'

r-l vt rH

m m o o

r^ oo ON o (N OJ <N «^

fvi <N CM CO

3

]

i

I I i I I

52

^^^f^lPI^^SS^ T#^■*■■■^^*«Wli.^fS9«WW*^«?:-■"w^■■■':■!^,:■ ■■ ■ .- -■

Typical devlatorlc stress and strain data from a

constant confining pressure trlaxlal test, a_ « 5 ksl,

are shown In Fig. 24. The curves are very nearly linear

at stresses less than approximately 30 ksl which Is the

level at which Initial yielding of the specimen occurs.

Also the unload curve Is nearly elastic with a very small

residual strain. Similar data was obtained from tests at

other confining pressures except the unconflned compression

test, cu ■ 0. For this test the slope of the devlatorlc

stress vs. devlatorlc strain curve Increased slightly an the

stress Increased meaning that the shear modulus, G, also

Increases with stress at low stress levels.

Tangent values of shear modulus, Gt, were determined

from the experimental data and are shown in Fig. 24 (b),

25 (b), 26 (b) and 27 (b) for specimen diameters of 2 in.,

4 in., 12 in. and 32 in. respectively. The stress paths

of the particular tests considered for each diameter are

shown in Figs. 25 (a), 26 (a), 27 (a), and 28 (a). As

observed from the data the shear modulus increases with mean

stress especially at the low stress levels. An equation

of the form

Gt - ca/'lO, (36)

in which "c" is a constant, was fitted to the experimental

results and is shown in Fig. 25 through 28. As relatively

little inelastic behavior was observed in the shear

deformations the model for shear modulus is the same for

both loading and unload-reload. Model predictions are in

agreement with observed behavior except at low stresses.

A summary of the mathematical models for bulk

and shear moduli along with the constants determined from

the experimental results is presented In Table 3. Values

of Young's modulus were computed from equation (30) using

the predicted values of bulk and shear modulus and are shown

lit RESEARCH INSTITUTE

53

■ ■• ■■■■■w.■■.,;. i

■ :■ - ■■ :■■■:.■, ■ ■ -,;■:.■ . . ■■

•rl CO

40

36

32

28

24

CO o I

CO CO 0) u

CO

o 4J CO •rl > 0) Q

20

16 -

12

8

Test No. 12 2 in. diameter

5 ksi Fracture

8 16 29 32 40 48

Deviator Strain, Cj^Eß, in/in x 10 -4 56

Fig. 24 DEVIATOR STRESS VS. STRAIN, CHARCOAL BLACK GRANITE

54

Wt^lSim^r^mm^,-^-.,-^ -■■■■■■'■■-■ :'■■:■■■-

Mean Stress, a,., ksi

a) Stress Path

16

12 on o

1 8

.3 | 4

Model (Unload-Reload) — ——-r--^-^^- Model ^^ 14 (Load)

Young's Modulus 12

1-1 14 Model


b) Shear Modulus and Young's Modulus

Fig. 25 TANGENT MODULI FOR CHARCOAL BLACK GRANITE, 2-IN. DIA.

55

imufc'vvmm i nsManwsMn »^îRe^wHMfrffîmsfi -. Wyf'j^fârmn^Krmfi^'K^'.rrrr^rt

32

24

16 •■-I

J2

.CM g

fe

Test 11

24 28


a) Stress Path

16

12

CO o

x 8

J2

§ 4 3 3

/

r ^-^Model (Load) Model (Unload-Reload)

^ ET

19

11

■^ "Model 19

J L 8 12 16 SO

Mean Stress, a , ksi in

J L 24 28

b) Shear Modulus and Young's Modulus


56

ISS' BW^S^S.WÄÄWfMlBRa^ vS3«^«ES«BS,MM!»l(¥^P^-w^if«^^!1-i-:^.vp^^^

32

24

16

J2

^

8

Test 16, 21

Test 20

0 4 8 12 16 20

Mean Stress, a) Stress Path

Mean Stress, a , ksl m

24 28

O

03 3 3

Mean Stress, a , ksi m

b) Shear Modulus and Tangent Modulus


57

^.■V;^: ■■:,. ^r.^^.i-^.^iu-;,.^;.,,,;

•"irrrnwrnrrowiimriiM^ imiinMniiPiiinii n.. uniii

24

16

5 8

4 8 12 Mean Stress

en o

•rl

CO

(0 3 3

16 — 28

12 ^/'"'

— — ■%

30

8 —

^ u 4

'Gt

1 1 1 l 1 4 8 12 16 18

Mean Stress a , ksi

Flg. 28 TANGENT MODULI FOR CHARCOAL BLACK GRANITE, 32-IN. DIA.

58

,,,,, MWRmmnrwr >

Table 3

ELASTIC PROPERTIES OF CHARCOAL BLACK GRANITE

Bulk Modulus

loading, kt - nAj1^ a. ^ m n

unload - reload, kt - nAg <?„,

Shear Modulus 1/10 loading, Gt - C ö^

unload - reload, G - C o

. G^ and 0m in ksi

1/10 , G^. and ai in ksi

Young's Modulus

9 \ Gt

Poisson's Ratio

V. 3 kt • 2Gt

Specimen Diameter in inches n

Al in ksi

A2 in ksi C

2 1.59 1.72 x 105 1.72 x 105 3,900

4 1.89 9.05 x 105 10.7 x 105 4,800 12 1.93 5.34 x 105 13.5 x 105 4,100

32 1.56 2.37 x 105

59

mmmrm»*

-■ i <m&mmmm

as a function of mean stress in Fig. 25 through 28. Poisson's

ratio values were computed from equation (31) and are shown

in Figs. 29, 30, and 31 for the different specimen diameters.

Again, except at stresses below 1 ksi the model fits the exper-

imental data.

5.3.2 Cedar City Tonalite

The nonlinear hysteretic model was fitted to the

various core sizes of Cedar City tonalite by use of log-log

plots of mean stress versus volumetric strain. The resulting

model parameters were used to compute bulk moduli in the

same fashion as was done for the Charcoal Black granite.

Figures 32, 33 and 34 show the actual bulk moduli as a

function of mean stress. The solid symbols indicate data

from the hydrostatic portions of the various tests, the open

symbols the triaxial compression portions. In general, the

hydrostatic data fall near the model and the triaxial data

depart from the model. The data points do not scatter

symmetrically about the model because the model was fit

to the volumetric strains rather than the bulk moduli.

The same observations apply to this data as to the

corresponding Charcoal Black granite data. The model for

each core size fits best in the intermediate stress ranges,

and the data scatter increases with specimen size. The

nonuniformity of this rock type is particularly noticeable

in the 12-ln. cores. Tests 17 and 38 had quite different

moduli below 5 ksi, but appeared to converge to the same

stiffness above 7 ksi. This may be expected if the existing

cracks are closing in this pressure range.

The scale effect is shown in Figs. 35 and 36. Figure

35 is a plot of the mean stress versus volumetric strain

predicted by the model for the three specimen sizes. Figure 36

is a common plot of the bulk moduli. The major difference between

the 2-in. and 4-in. models is that the 4 in. model is slightly


60

0.5 I—

o l! 0.4 5 ? 0.3 c o CO

.2 0.2 ,2

o.i

0 Test 12 A Test 14

O Test 34 2" CBG

^r V ZModel

0 10 20 30

Mean Stress (ksi)

40 50

0.5

.2 0.4

« 0.3 "c

1 0-2 •i-i

o.i

o D

Test 9

Test 11

Test 19

o o

Model

4" CBG

10 20 30

Mean Stress (ksi)

40

Fig. 29 POISSON'S RATIO VS. MEAN STRESS FOR 2 IN. 0 AND 4" CHARCOAL BLACK GRANITE

61

mmmmm wmmfmmmmmmmmmmmmmmm •""»(««»«««»««»««SBW^^^äW^i»«^

.5

.4

.3

.2

.1

A

A Oeo^

D CP

0 Test 16

A Test 20

D Test 21

12" CBG

Model

10 20 30

Mean Stress (ksi)

40

Fig. 30 POISSON'S RATIO VS. MEAN STRESS FOR 12" (3 CHARCOAL BLACK GRANITE

.5 0 Test 29-30

.4

.3

AA A Test 27-28

.2 4 y* -^

.1

| |

0 10 20 30

Mean Stress (ksi)

40

Fig. 31 POISSON'S RATIO VS. MEAN STRESS FOR 32" 0 CHARCOAL BLACK GRANITE

62

1 --■ niiTMlftMWIIWMiMMWrtlWMr.lLHUUIJ I...

O

CO X

CO 3

i-i

3

r-l

3 03

2-in dia. tonallte

25 26

O " 33 SHADED SYMBOLS INDICATE HYDROSTATIC. STRESS .STATE

x 10 = 5 ksi

5 10 "

15 "

8 10 12 14 16 It? 20 22 24 26 28 30

Mean Stress, J^ ksi

Fig. 32 BULK MODULUS FOR 2" CEDAR CITY TONALITE

o

■r-l [0

CO 3

3

7

6

5 -

4 _

3

2

4-in. dia. tonalite SHADED SYMBOLS INDICATE HYDROSTATIC STRESS STATE

- D O

- ^ A ^7 fn = 1 .37

— D

D c ▲ A^^f/iAi= 1.77 x lO"1

— V

G0 V z ▼ v S^b / «Test 36 5 ksi

35 5 "

1 mo&k ̂ ^T^ A ^ ^ 18 10 "

J 1 ,

^ o o

1 1 1 i -L 1 1 1 1 1

22 15 "

23 15 "

1 1 2 4 6 8 10 12 14 16 18 20 22 24

Mean Stress,o„,. ksi tn'

Fig. 33 BULK MODULUS FOR 4M CEDAR CITY TONALITE

63

*,ie.m!mm*mm,™mrmm^

CO o 1-1

•o

pa

6

4

3

2

X 3 H

CO

(0 3

O Test 17 5 ksi

O Test 33 10 ksi

b = 1.32

2-in. dia. tonallte o

SHADED SYMBOLS INDICATE HYDROSTATIC STRESS STATS

= 2.08

10 11

Mean Stress, (?„,, ksi

FIG. 34 VARIATION OF BULK MODULUS FOR CEDAR CITY T0NAL1TE, 2-in, 4-in. and 12-in. DIAMETER

22 — A"

20 —

18 — 24" /

16 — /

| 14 __

B12 —

CO

g io U 4J w 8

c v 6

2u

—

//

/ 12"

V 4 — y /

2 — y^^

1 1 1 .002 .004 .006

Volumetric Strain

.008 .010

Fig. 35 VOLUMETRIC STRAIN FOR CEDAR CITY TONALITfi MODELS

64

o

f-i CO

3

3 CO

5 Immm

4 __

3 — _-— —'2

2 ^^ ̂ ^ - 12

1 €^ -^

V\ 1 1 i 1 1 L 1 1 0 6 8 10 12 14 16 18 20

Mean Stress (ksi)

Fig. 36 BULK MODULUS FOR CEDAR CITY TONALITE MODELS

65

»Llfler below 3 ksl. This results in a horzontal displscement

of the curves in Fig. 35. If Fig. 35 were extended to higher

stress levels, the 2-in. and 4-in. curves would cross as a

result of the higher 2-in. bulk modulus. The actual differences

in these curves are probably a result of specimen variation

rather than scale effects. The 12-in. specimens appear to be

significantly less stiff than the smaller specimens.

Figure 37 shows the scale effect upon shear modulus

G and elastic modulus Et. Data from all tests are included,

and again the scatter is caused by the short interval between

data points. It can be seen that the 2-in. and 4-in. specimens

were not significantly different, and that the 12-in. specimens

were less stiff at lower mean stress values. The shear modulus

did not fit the one-tenth power of mean stress model, so fair

lines were passed through the data by eye. The elastic

modulus model was computed using values of the bulk modulus

models in Figs. 32, 33 and 34, and appears to represent

the experimental elastic moduli well.

Figure 38 shows plots at Poisson's ratio for the

various size specimens. The typical behavior is to start

out somewhat below the model and rapidly increase to a

value greater than would be predicted by this model. The

tests having 15 ksi confining pressure maintain a value

of approximately 125% of the model value for a period before

yielding begins, while the tests at lower confining pressures

appear to maintain a monotonic increase. As the yield point

approaches, the value of Poisson's ratio may increase because

of the dilatancy of the specimen.

5.3.3 Uniaxial Strain Tests

Uniaxial strain tests were conducted on two specimens,

a 22-in. dia. Cedar City tonal!te specimen and a 32-in. dia.

Charcoal Black granite specimen. The results from this type

of test should be applicable to unidirectional compression

llf RISIARCH INSTITUTE

66

t^m^mr^m---.:-^-'-■:--:^-->^;/^^'^^^^M^^-^^'i ■■■• i. . ■ ■.:'i*-iI-1».»|,".-»-«fr,-p..tf.- ■:-.r.VI^i.l. ■■..■ .

C=r = r= z z z

< " HCVICMCM^r«*»* stCM CM Q r-i r-t

H W W H

< O > • ^ ► + K

o m

•X) CM

w vO 1^1 <N ä <t § CM H

CM S CM •H H

(0 O M

O §t ^ B

o 3 OC o ^-1 n

«5 Oi (0 o

X) dJ (K <-* ^ 4-1 l-l to ->

>* D f-l C O

CO Q Ä s

CM

00

vO

CM

S O

en

00 •i-i

vC IT) m CM

.01 x jBy[ «'o JO ^a 'TTnP0W

67

■ mmmmmmmmmmmmmmmm ■■iiwiwumMiMiiii mmmmmmmmmmmmimmm

5 \-

(0

1 D 25 • ■ 5 ksi

| 0 26 • • 10 ksi L A 33 - • 15 ksi

3 h-

2" 0 CCT AA

c o w

2(3kt - G,.)

I I I I 6 8 10 12 14 16 18 20 22 24 26 28 30

Mean Stress (ksi)

.5h- D 35 - 5 ksi O 36 - 5 ksi N7 22-15 ksi

15 ksi

4" 0 CCT

O 4J to

.4 _ A 23 - ]

co .3 — 'c o

(0 .2 — (0 •H O 0, .1

1 |D

° o

OocPD 0

-B

V 2^

s^^7

^

I I I I J i i I I 6 8 10 12 14 16 18 20 22 24

Mean Stress (ksi)

u . co .4 06

.M.3 B O co 9

•I-I

S.l

A 17

O 38

5 ksi

10 ksi 12" 0 CCT

I I I 2 4 6 8 10 12 14 16 18 20

Mean Stress (ksi)

Fig. 38 POISSON'S RATIO FOR CEDAR CITY TONALITE

68

■MmmmMMmntaffi .m^M^ummmmmw^'r^'--,-^. ■■ ■--■■■■■..■..■■...■.■v'

of an element in a rigidly confined mass or plane-wave

propagation. The radial strains were monitored during the

test by the auxiliary averaging strain gages described

in the experimental apparatus section of this report.

Confining pressure was controlled to maintain these gage

readings as near zero as possible.

Figure 39 shows the axial and lateral strains and

the stress trajectories for both tests. As can be seen,

the radial strains did go tensile by about 250 micros trains

in test 31 and 100 micros trains in test 32. The Cedar City

tonalite (test 32) failed at an axial stress of 20 ksi.

The behavior of the Charcoal Black granite was

somewhat more complex, primarily because this specimen was

able to support load after slippage, and the test was

continued for two full cycles. The offset on the unload

cycle at 11,5 ksi was caused by a gage failure. The offset

on the reload cycle at 26.5 ksi was accompanied by a major

rock shift.

Figures 40 and 41 show the shear strain and volumetric

strain for both tests. Note that for this test condition

there appears to be little difference between the two rock ft ft

types. Both have shear moduli G between 4 x 10 and 5 x 10 ,

Any curvature in the Charcoal Black granite shear modulus

is swallowed by the initial zero offset, which may or may

not be real. The bulk modulus for the Cedar City tonalite 6 fi

increases from 1.6 x 10 to 5.2 x 10 ksi as mean stress

goes from zero to 9 ksi. The Charcoal Black granite bulk fi ft '

modulus ranged from 1.7 x 10 ksi at 1,5 ksi to 4 x 10 ksi

at a mean stress of 10 ksi. Corresponding values for elastic

modulus and Poisson's ratio are listed below:


69

I

) '■

I

I

■"■'••■■■"•■■

Test 31 CBG

0 4 6 8 10 12 14 16

Mean Stress (ksi)

Lateral Strain .001 .002

Axial Strain 003 .004

Fig. 39 UNIAXIAL STRAIN TEST

70

wraww^"-?-*^«^^^^^

30 i—

03 (0 01 U 4J w M O 4J (0

•■-< > <u a

20

10 —

16

.002 .003 Shear Strain

Fig. 40 SHEAR BEHAVIOR FOR UNIAXIAL STRAIN TESTS

•i-i

to

CO (0 <u u u M

0)

1^

12

10

8

Test 32 CCT

.002

T" .002

Unload Cycle Two

1 1 .004 .006 .008

Volumetric Strain

Fig. 41 VOLUMETRIC STRAIN FOR UMIAXIAL TEST

71

—"" TnTT^'in'TI'ITrTirTriMliHIMM

Charcoal Black Granite Cedar City Tonalite

% G K E V G k • E V

2 4 2.9 8.3 1 .03 4.5 3.5 9.5 .05

4 3.3 j 8.5 .07 4.4 10 .12

6 3.8 8.9 .11 j 7.0 11 .24

8 4.2 9.1 .14 10.5 12 .31

5.4 Strength Properties

Figure 42 indicates the maximum stress levels attained

by each specimen. Due to a less favorable intensification ratio

in dhe 14-in. triaxial eel?, there were no failures of the 12-in.

specimens. Future programs would need to employ higher stress

levels to insure failure.

The 32-in, dia. Charcoal Black granite specimens reached

maximum stress levels of about one half that of the 2-in. specimens

The actual scale effect is probably somewhat greater. Slippage

along a joint plane will produce instant failure in a 2-in,

specimen, while a 32-in. specimen not only survives minor slippage,

but can be loaded to greater stress levels.

The Cedar City tonalite was much more variable. As

might be expected from a weathered rock, the strength at low

mean stress levels is quite low. This corresponds to a low "c"

value on a plot of the Mohr-Coulomb failure envelope.

Enough data was not obtained in this program to apply

any statistical theories, such as those of Weibull or 15

Grobbelaar . It is hoped this will become possible when more

data is accumulated.


72

• ■■■..■■ ■ ■ ■ :■■.-■■ ■.■■.

30

J? 20-

? 10 —

Charcoal Black Granite

0 Solid Symbols Indicate Failure

#

D

— J Symbol

O Dia. 2"

0 / ♦ D D 4"

* A

1

A

i o 12"

32" o 1 1

0 10 20 30

Mean Stress (ksi)

J

30 _ Cedar City Tonalite

Solid Symbols Failure

Indicate 0

20 ■

• D Symbol

O Dia. 2"

10

■ D D

A

4"

12"

Qh V 1 1

O 24"

1 10 20 30

Mean Stress (ksi)

40

Fig. 42 MAXIMUM VALUE OF Vj]" REACHED FOR ALL TESTS

73

wmwhmtmw&zmfymmmmmimM wmatm/K *Mmmm

I

I

6. SUMMARY AND CONCLUSIONS *

Over the course of this program, 27 trlaxlal tests | were run on samples ranging from 2 In, to 32 In. dla. This Is the first time that specimens of this size have ever been tested under laboratory conditions. Because of the large volume of data collected, the results of this program _ are presented In term of a nonlinear hysteretlc model proposed J by Seaman and Whitman^ and having the form

] "in " Vv loa<lln8

"m " A2(ev"evpn unloadln8 1

. ..„.. ]

i i i I

a_ Is mean stress m e Is volumetric strain

e , Is residual volumetric strain.

The data fit this model well at Intermediate stresses. However, the model predicts that bulk modulus Is zero when mean stress equals zero, and bulk modulus goes to Infinity at Infinite mean stress. In fact, rocks display a finite bulk modulus at zero mean stress and a constant bulk modulus under high stresses. In spite of this, the data depart from the model only below stresses of about 3 ksl and f at higher stresses when yielding occurs.

I The model parameters as fitted to each core size are summarized In Tables 4 and 5. Up to 12-in. dla. it seems the Influence of specimen size on the mechanical ¥ properties is small. There is not enough data on the larger samples to draw definite conclusions. The largest scale 'M effect was found in the Cedar City tonallte at mean stress levels below 5 ksl. Both the model and the experimental data indicated low bulk modulus and elastic modulus in this

IIT RISEARCH IN8TITUTI

74

I

MKMHlMIMBmmWWMßHWM^^ -'l:'.;.'.■': ^V'1 1:"'

range, although these parameters increase rapidly with mean

stress.

The Influence of specimen size on strength Is

pronounced on both rock types. The 32-In. Charcoal Black

granite specimens failed at stress levels about one half

those of the 2-in. specimens. The mode of failure also

was markedly different. The 2-ln. specimens failed

catastrophically, while the 32-in, specimens failed initially

by a series of small slips.

With the accumulation of more test data it may

become possible to develop a model which more clearly

predicts the behavior of the large rock cores. It may

also become meaningful to verify statistical hypotheses.

It should be noted that with the larger cores, the

rock depicted a load carrying capacity even after failure

had initiated. This is often observed in the field. Besides,

the mechanism of failure was different in these larger

cores. This is Significant in that at about 30-in. die.

or larger perhaps the type of rock failure obtained appears

to be similar to that observed in the field. Perhaps models

developed for this size can predict results closer to field

observe tiooa.


75

^»vsmmmmmmmmimmmm

0)

Xi

I vO SO rs cn o CM <M O o en H m CM f-l CM Os < <-! CM H i-4 r* CM O SO

« • * « • • • U • o o i-l H o CM CO O

00 e

00 en «* so ON d) i-4 <* o 1-1 ON «* m H ON CM s 00 *• O oo

HvO M i-l i-4 CM CM CM i-l o •H cn CM OS SO < o j « • • • • • • • u • • • • I

H O o i-l i-4 O i-l 0) o O i-4 H j X 0.

(0

•o 0)

e i-J CM cn SO O i-4 00 en •o oo en m m 0

C SO in so 00 OS sO o> o s r^ m oo o 00 • • »

i-l H • 1

i-l H •

i-4 •

1-1 •

CM 0

1 • • • •

H f-4 ** * 1

^ L " r 3 PQ «O

0 m s » m o m m m m O m m o o , cn •J iH H i-l r-4 «-» lu

S V (tf 1

1 w (0 cs <* .* OS fH OS sO r** f-i O 1^. 00 OS O i-4

£ i-4 f-i cn fH f-4 •-4 cn CM CM CM CM CM cn cn

^ «

1 -u CM «* CM

i-4 CM en

•r« -■ 1 Q >

76

: ■ ,; ; .■...■ ■. ■■ ■ . ■ . . ■

m 0)

i-4

5

m 1 o

m a» CO m 00 iO CM CM

i-4 • • • SO H

X CM 1 ^

m o to m so CM i »"", vD vo i-4 m m m co CM SO

m O 00 ON oo r» o 00 ** 1^ O X o m <*i H H *• f4 O co '-4 i-4

<

00 ** o co ts. co m St •D CM 00 \ i ö CM vO vO <f CM CM CO vO co CO O

r-4 H H H H i-4 H 1-1 i-4 r-l CM

i ^ o m mom m m o m m m O i ^ H H i-4 t-4 r-l H Iw

4J w ^d- m vo co m so oo CM CO r^ oo CM 0) <M CM CM CO CO CO 1-« CM CM i-4 CO CO H

^ 0) 4J

CM ^i- CM •4* i 1 CD r-l CM j 1 *^

1 1 Q

77

inWfTO^tJTOwwtwff^^wiH^

REFERENCES

1. Rapid Excavation, National Academy of Sciences, Wash. D.C.,

Publ. 1690, 1968, 48p.

2. Proc. Advisory Conference on Tunneling, Rept. on Tunneling.

1960-1980, Organization for Economic Cooperation and

Development, Washington, D.C. June 2?-26, 1970, 26p,

Appendices and Comments.

3. Standard Method of Test for Triaxial Compressive Strength

of Undrained Rock Core Specimens Without Pore Pressure

Measurements, ASTM Test Designation D2664-67.

4. Standard Method of Test for Direct Tensile Strength of

Rock Core Specimens, ASTM Test Designation D2936-71.

5. Standard Method of Test for Unconfined Compressive Strength

of Rock Core Specimens, ASTM Designation D2938-71.

6. Standard Method of Test for Deformation Moduli of Rock

Core Specimens in Compression, ASTM Test (In Preparation).

7. Rice, G. S. and Enzian, C, Tests of Strength of Roof

Supports Used in Anthracite Mines of Pennsylvania,

U. S. Bureau of Mines Bull. n303, 1929, 44p.

8. Greenwald, H. P., Howath, H. C, and Hartmann, Experiments

on the Strength of Small Pillars of Coal in the Pitts-

burgh Bed, U. S. Bureau of Mines Tech. Paper n605,

193?, 22p.

9. Burton, L. D. and Phillips, J. W., Communication to

Evans and Pomeroy (11).

10. Mlllard, D. J., Newman, P. C. and Phillips, J. W.,

The Apparent Strength of Extensively Cracked Materials,

Proc. Phvs. Soc. (London). v68, ser B, 1955, p. 723-728.

11. Evans, I. and Pomeroy, C. D., The Strength of Cubes of

Coal in Uniaxial Compression, Mechanical Properties

of Non-Metallic Brittle Materials, ed. W. H. Walton, III IISEARCH INSTITUYI

78

<ff^<mmmii^mi»mm-' ■ . ,.<M-,———————

Interscience Publishers, New York, N.Y., 1958,

p. 5-28.

12. Holland, C. T., The Strength of Coal in Mine Pillars,

Proc. Sixth Symp. on Rock Mech.. U. of Missouri at

Rolla, Rolla, Mo., 1964, p. 450-466.

13. Weibull, W., A Statistical Theory of Strength of Materials,

Ineretensk Akad. Handl.. nl51, 1939, p. 5-45.

14. Protodyakonov, M. M., Methods for Evaluating of Cracks

and Strength of Rocks in Depth, Fourth Intl. Conf.

Rock Mech. and Strata Control. Columbia U., New York,

N.Y., 1964, Addendum.

15. Grobbelaar, C, A Theory for the Strength of Pillars.

Pillarco, Pretoria, S. Africa, June 1970, 103p.

16. Epstein, B., Statistical Aspects of Fracture Problems,

Jour. APPI. Phvs. v 19, n2, Feb. 1948, p. 140-147.

17. Bieniawski, Z. T., Mechanism of Brittle Fracture of

Rock, D.Sc (Eng.) Thesis, U. of Pretoria, S. Africa,

1968.

18. Glücklich, J., Cohen, L. J., Size as a Factor in the

Brittie-Duetile Transition of Some Materials,

Int. Jour, of Fract. Mech. v 3, n4, Dec. 1967, p. 278-289.

19. Glucklich, J., Cohen, L. J., Strain-Energy and Size

Effects in a Brittle Material, ASTM Materials

Research and Standards, v 8, nlO, Oct. 1968, p. 17-22.

20. Baecher, G. B., The Size Effect in Brittle Fracture,

M. S. Thesis, Mass. Inst. Tech. June 1970, 190p.

21. Swanson, S. R., Development of Constitutive Equations

for Rocks, Ph.D. Thesis, Univ. of Utah, Dec. 1969, 140p.

22. Adams, F. D. and Nicholson, J. T., An Experimental

Investigation into the Flow of Marble, Phil. Trans.

Roy. Soc. (London). Ser. A, v 196, 1901, p. 363-401.


79

23. von Karnwm, T., Festigkeitversuche unter Allseitigem Druck, Zeitschr. des Vereins deut. Ing.. v 60, 1911, p. 1749- 1757.

24. Griggs, D. T., Deformation of Rocks Under High Confining Pressures, J. Geol.. v. 44, 1936, p. 541-577.

25. Griggs, D. T., and Miller, W. B., Deformation of Yule Marble: Part I—Compression and Extension Experiments on Dry Yule Marble at 10,000 Atmospheres Confining Pressure, Room Temperature, Geol. Soc. Am. Bui., v. 62, 1951 p. 853-862.

26. Handln, J. W. and Griggs, D., Deformation of Yule Marble: Part II—Predicted Fabric Changes, Geol. Soc. Am. v. 62, 1951, p. 863-886.

27. Griggs, D. and Handln, J., Rock Deformation. Geol. Soc. Am.. Mem. 79, March 1, 1970, 382p.

.28. Baidyuk, B. V., Mechanical Properties of Rocks at High Temperatures and Pressures. Consultants Bureau, Plenum Pub. Corp. New York, 1967.

29. Morgenstern, N. R. and Tamuly Fhukan, A. L., Non-linear Stress-Strain Relations for a Homogeneous Sandstone, Intl. Jour. Rock Mach. Mng. Sei., v. 6, 1969, p. 127-142.

30. LaMori, P. N., Static Determination of the Equation of State of Cedar City Tonalite, DASA Rent. No. 01-69-C 0053, May 1970, 78p.

31. McClintock, F. A., Walsh, J. B., Friction on Griffith Cracks in Rock under Pressure, Proc. 4th Nat. Cong. Appl. Mech., Berkeley, 1962, p. 1015-1022.

32. Brace, W. F., Brittle Fracture of Rocks. Proc. Intl. Conf. on State of Stress in the Earth's Crust. American Elsevier Publ. Co., New York, 1964, p. 111-174.

IIT RESEAICH INSTITUTE

80

WMBBIiyiMIIIJIIIIIWIM ' '

i

33. Murrell, S. A. F., The Effect of Trlaxlal Stress Systems on the Strength of Rocks at Atmospheric Temperatures, Geoohvs. Jour., v. 10, 1965, p. 231-282.

34. Pfefferle, W. and Smith, C. R., Phase I Flatjack Tests, Air Force Rept. No.: SAMSO^TR-70-381, Oct. 6, 1970, 42p.

35. Obert, L., Personal communication.

36. Hoek, E., Brittle Failure of Rock, Chapter 4 in Rock Mechanics in Engineering Practice (ed. Stagg and i Zienkiewicz), J. Wiley, London, 1968, p. 99-124.

37. Wawersik, W. R., Detailed Analysis of Rock Failure in Laboratory Compression Tests, PhPD. Thesis, , University of Minnesota, 1968.

38. Cook, N. G. W., The Failure of Rock, Int. Jour. Rock Mech. Mng. Sei., y. 2, 1965, p. 389-403.

39. Houpert, R., La resistance a la rupture des granites, i Revue de 1*Industrie minerale. kaylS, 1968, p. 21-23.

40. Paulding, B. W. Jr., Techniques USed in Studying the Fracture Mechanics lof Rock, Testing Techniques for Rock Mechanics. ASTM STP 402, Am. Soc. Testing Mats., 1966, p. 73-86. ,

i i

41. Clark, G. B., Deformation Moduli of Rocks, Testing

Techniques for Rock Mechanics. ASTM STP 402, Am.

Soc. Testing Mats., 1966, p. 133-174. , ,

42. Ko, Hon-Yinn, and Scott, R. F., Deformation of Sand

in Hydrostatic Compression, Journal of the Soil

Mechanics and Foundation Division. ASCE, vol. 93,

No. SM3, l^ay, 1967.

43. Timoshenko, F., and Goodier, J. NJ, Theory of Elasticity.

McGraw-Hill Book Co., New York, 1951.

i i i < • ! i i


81 :

-"■ -"««■»•«^"^»'^^■-'«»■W^

44. Seaman, L., and Whltnum, R. V., Stress Propagation

in Soils, Final Report-Part IV, Stanford Research

Institute, Menlo Park, California, for Defense

Atomic Support Agency, DASA 1266-4, June 1964.

45. Birch, F., and Bancroft, D., The Effect of Pressure

on the Rigidity of Rocks. Jour. Geol. v 46, nl,

Jan-Feb 1938, p. 59-87; n2, Feb-Mar 1938, p. 113-141.


82

^■»«f»««»«!«««»-«»»!««^^ .rumammrn^-vr^raa ■

APPENDIX A - COMPUTER PLOTS OF TEST DATA

Data was reduced and plotted using the Unlvac 1108 at

IITRI. This appendix Includes the three most significant plots

for each test, these being:

shear strain vs. deviator stress

volumetric strain vs. mean stress

axial and lateral strains vs. axial stress.

In several cases, e.g. test 19 a vs. e„, the data went off- 0 m v scale during the plotting subroutines. When this occurred, the

data was plotted at an arbitrary value within the plot scale.

The plots are arranged In order of rock type, core diameter, confining stress and test number.

Rock Tvne Diameter Confining Stress Test Page

CBG 2 5 12 A-3 10 14 A-6

15 34 A-9

4 5 9 A-12

10 11 A-15

15 19 A-18

12 5 16 A-21

5 21 A-24 5 37 A-28

10 20 A-31

32 5 27 A-34 5 28 A-37

10 29 A-40 10 30 A-43

unlaxlal strain 31 A-46


A-l

:„;;;.;;■, :': .:, ■ ■■ ■.. ■ ■.■ !' . ■■■■ ■

■■■■- ■■'..■■■ . . .

■•.*- - :". ' .--.... ....

Rock Type

CCT

Diameter

2

12

24

nonflntng Stress Test

5 24

5 25

10 26

15 33

5 35

5 36

10 18

15 22

15 23

5 17

10 38

uniaxlal strain 32

Page

A-49

A-52

A-55

A-58

A-60

A-63

A-66

A-69

A-72

A-75

A-78

A-81


A-2

um ^g^jWgMWiwsfmttH1' mmmmmw*

o

cn

IT!

o

a ■3-

(M-

cn

co UJ QC

CO

et:

h-- a- i—i

>

Q • Lp

o

TEST NUMBER 12 DlfldETER 2 [N CONFINING PRESSURE 5DQQ LHflRCORL SLRCK GRRNETE

PS[

■ID.00 D.QO

SHERR iU.DD

STRAIN 20.00

MICRO-

T 3 0.Q0 M0.00

STRniNS(XlDt*2)

\ 50 .00

A-3

'■mm>m>mmMmm»m^^mi>m^wmmsm'vm^mmmmmmmmmmmmmi

en en

CJ f

3" '1 i-vl

0\J

cn

cp-

CO ÜJ

I— cn co

z CE LÜ ST

CV —

o cn

CD cn

TEST NUMBtR I'2 DlflflETER 2 CN CDNFINING PRESSURE 5DD0 PS I CHRRCDRL. 3LPLK üRflNITE

'-10.00 O.QQ

VOLUMETRIC

I I I I I VD.OD 20.0D 3Q.00 40.00 5D 20.0D 30.00 40.00 5D.00

STRRIN MTCRO-STRRINSCXIO**?)

I 1 I I I i i i I i I I

A-4

nwms&tmmtmi aww» .-

-^ 1

1-p u-.

CD

IT'

CM •

CO UJ cr |— o CO 0

T ■

CT .- -I

X (To

o

«-1

cs o

o

TEST NUMBER

DIAMETER 2 [N CONFINING PRESSURE 5D0D LHRRCOflL BLACK GRANITE i AXIAL STRAIN

♦ LRliÄflL STRACN

PS[

•ID .00 T

0 .00 ID .00 20 .00 30.00 MD

STRREN *11CRO-STRRINS(X10^2) 0D

I 50 .00

A-5

o

o o

w

n

to *S coS Lü

a

o2 ^- cc In«

Ss

TEST NUMBER DIAMETER 2 IN CONFINING PRESSURE 10 000 CHRRCORL BLRCK QRRNITE

it

i •10,00

T r COO 10.00 10.00 10.00 ilO.OO SHEAR STRAIN MICRO-STRAINSCX10**2)

so.oo

A-6

1 i

o o

<N- CO

OJ

CM

CO

u

0)

«>•

CM

CL LÜ z:

o o

TEST NUMBER DIAMETER 2 IN CONFINING PRESSURE 10000 CHflRCOflL BLACK GRANITE

-10.00 0.00 VOLUMETRIC

10.00

STRRIN 20.00 30.00 HO.00 50

MICRO-STRflINS(X10in>2) oo

A-7

I

psr

-10.00

TEST NUMBER DIRMETER 2 tN CONFINING PRESSURE 10000 CHflRCORL BLRCK GRRNITE + RXIflL STRfltN ♦ LRTERRL STRREN

! j 1 ! !

0.00 10.00 20.00 30.00 MO.00 50.00 STRRIN MICRO-STRfiINS(X10t+2)

A-8

■

(0 a .

h-

(E i—i

+ ■H-

TEST NUMBER 34 + DIflHETER 2 IN CONFINING PRESSURE 15000 PSI * CHflRCORL BLflCK SRRNITE +

+ +

+ + +

+

+ +

+

+ +

•••

++ + +

-.{> , , , , , , ni.OP 10.00 CO.00 30.00 40.00 50.00 so .00

SHEAR STRRIN MICRO-STRflINSCX10^2)

A-9

et*

M

M

Ul

'<n*A

UJ

f

[ +

+

i f

+*

I TEST NUHBER 94 * OimETER 2 IN ♦ C0NFININ6 PRESSURE 15000 P8I ♦ CHRRCORL BLRCK 8RRNITE +

■f

♦♦

+ +

^—-^j -,_ .,_ T_,— Lj *■ n ^.00 id.00 £0.00 30.00 40.00 80.00 SO .00

VOLUMETRIC STRAIN MICRO-STRflINS<X10^2)

A-10

1

mmmmmmmmmmmmmmm*™* ... m . . . ■ ■•'■'• ,

cog

T ÜJ

I—l'

X (Ee

A

A

A

4

-+ + +

+ TEST NUMBER 34 * OIRN^TER e IN + C0NFININ6 PRESSURE ISOOO+PSI CHflRCORL BLfltK GRRNITE + ftXIflU STRAIN A LRTERflL STRRIN

+ ++

. , - +++

+

+ ++

/

—i——~"T r—; 1 ~—i '-10.00 0.00 10.00 20.00 90.00 40.00 SO

STRAIN HlCR0H8TRniNSCX10^2) 00

A-ll

m 1J ■^■»;9KW9w»fflfia(i waiSI!^MIiirillWW'JIMIW!«Bl--miWiaMI

CM'

eo ■ CM

T ■ CM

O

CM

TEST NUMBER DIflflETER 4 .00 IN CONFINING PRESSURE CHflRCORL BLACK TEST

10 PS I (DRY)

CO

o co«,-- LÜ ct: •r-

o ct: ■ OS'

> LÜ Q

a o

-10.00 0.00 10.00 20.00 30.00 HO.00 SHERR STRRIN MICRO-STRRINSCX10t*2)

50.00

J A-12 I

'■■■■'■'''■^^^^BlUm m^smmmfk-^sw-hn ■.:■■ ■ ' :..' -. ..■ ■...-.., ;; ;;,:,,, , : .: ...... . , ,. , ,.,.. .; .,.,....,,,.,

a- OJ

a in

UT

o

CM-

"^ o CO o

^o-

CO " CO ÜJ

CO«1.

z CE UJ 21

a o

in

o in

eg

o o

TEST NUMBER 3 DIAMETER 4.00 IN CONFINING PRESSURE CHflRCQflL BLACK TEST

500D PS I I «DR^O

-10.00 0.00 10.00 20.00 30.00 40.0C

VOLUMETRIC STRRIN MICRO-STRRINSCX10**2) 50.00

A-13

.-.:.,-. ■ . .>,-. :■ ■ ■

*»«M*»a':*K5>>*^^^^^

«3-1

en

en

D i I I I i I

TEST NUMBER 9 DIAMETER 4 ,00 IN CONFINING PRESSURE 50DD PS[ CHflRCQHL BLACK TEST I (DR^f) »• AXIAL STRAIN

■» LATERAL STRAIN

-10 .00 T

0.00 ID.00 20.00 30.00 H0.Ü0

STRREN M[CR0-STRRINS(X10-**2)

A-14

50.03

«iniii irinniii—nm mi.

-Vr-i.- ■-■■■- : ■ ■; ^■-.- -■-. :■ ■■■:■■ ■.'"■■ ' •:■■■ '-■-.' ■:-: -.. ■ ■

o

CD

10 ■

C3 cn

CO

UJ or.

o ! CK ■ I

I—

Q • !

o

O O

TEST NUMBER QtaiETLR H [M

CQNFINENG PRESSURE iDODD CHflRCDRL 3LRLK ÜRflNITE

iO .00 0 ,00 T

iDOD 2D.DO 3000 A0 $0

SHEAR STRRIN MICRO-STRRINS(Xi0t*2)

1 50 QD

A-15

w%fäff8ßfi?M&iiiwtm*Mi9r**$*%&*?***''im-™

o

rn

3- •

C3 ■

o

CO LO Lü &.

z: UJ

14?-

^N-

o o

O

o

TEST NUMBER 11 DlflMErER M [H

L'QNflNING PRESSURE iOOOO PS I LHflRLDflL 3LRCK GRANITE

■10.00 0.0D

VOLUMETRIC 00

STRRIN

I ! " I 1 20.00 30.00 MO.00

MICRO-STRRINS(X10t*2) 50 .00

1 I I }

I 1

&

E I I

A-16

D

llBlB^^)WWP'|^<ww''^'^'fa'^*'!^•^';^•"'■''••-•■•■ ■' ■■■■■

TEST NUMBER U D I.«METER ;! :N CDNftNING PRESSURE iDDOO LHRRCDRL BuRCK GRRNITE > RXTRL STRR[N ♦ U.RTERRL STRRTN

PS I

-ID ,00 0 .00 STRPIN

i ~r 10 , oo io

M T. CRO-S TRfl INS (X1 Q t ♦ 2 ) on

—i 5 0 00

A-17

tmmmiimmwmamm

o Cvj

o

in

CO

o

(— CO

a ct: •"

> LJ

CM

TEST NUMBER DIAMETER 4 IN CONFINING PRESSURE 15000 CHRRCOflL BLACK GRANITE

-50 .00 0.00 SHERR

50.00 STRRIN

_! --..j

100.00 150.00 2D0.OÜ MICRO-STRRINSCX10++1)

250.00

A-18

mMmniffiHWiim "■■ ■ '

IN-

co-

CM

O

CM

CO o

LO LO LU cr m z. CE

z:

<J0-

C3 o

o

CO

o o

TEST NUMBER 13 DIAMETER M [N CONFINING PRESSURE 15DOP CHflRCORL BLACK GRANITE

PS[

-50.00 0.00

VOLUMETRIC

i r 50.00 100.00 150.00 200.00

STRRIN MICRO-STRRINS(X10**1) 250 .00

A-19

^W'H^fSWl

\

o o ■

o en

ir>- m

TEST NUMBER DIHMETER 4 IN CONFINING PRESSURE 15D00 CHflRCOflL BLACK GRANITE + AXIAL STRAIN ♦ LATERAL STRAIN

PS I

-50 .00 0.00 50.00 100.00 150.00 200 STRRIN MtCRO-STRfllNSCXlCH+l)

oo i

250 00

\

A-20

«■- rWPOMWt«

-50.00 50.00 100.00 150.00 200 SHERR STRRIN MICR0-5TRRINS(X10

oo 250.00

A-21

KtmmwmHammmmmtmm

o

3" ■

O

O

TEST NUMBER U DIAMETER 12 EN CONFINING PRESSURE 5000 PSI CHRRCOflL BLACK GRANITE

-50.00 0.00 50.00 IDO.OO 150.00 200.00 250.00 VOLUMETRIC STRRIN MICRO-STRRINSCX10+*!)

A-22

y^bWtöfäB&sm/mmmtmm

CO

EST NUMBER 16 ' DIAMETER 12 IN , CONFINING PRESSURE 5ODD PS I CHflRCOflL BLACK GRANITE + AXIAL STRAIN ♦ LATERAL STRAIN

0.0D 50.00 100.00 150.00 200,00 STRRIN MICRO-STRRTNSCXlO^+l)

250 .00

A-2 3

u m I -SÜ. ., ,-■„.= .. r...„y.w,-,-«

■ I I'lilliiWMIiiwWjIPWIBIWIIWWIIWWIIIWWWI^IiHMBPIlWlt'TWIII'ffiTl'WWWIWfMllfHnM^

o- <M

CD in

CD

ir- ,

TEST NUMBER DIRMETLR IQ [N CONFINfNS PRESSURE CHflRCQflL BLACK GR.

5(100 PS (RELQflD lb)

CO

CD

CO -■• ixl or h-

o

h- CC

> LLl0 Qo

in

in

o

J

1 I

I I

■50.00 0.Q0 50.00 100.00 150.00 200.00 SHEFIR STRfl[N M [ CR0-£TRRINS(X10**1)

250 .00

A-24

a o

a o w

o I a 1

TEST NUMBER 71 DlflMETER l^ tN CIMr:N(NG PRESSURE CH^RCORL BLACK GR.

5000 PSI (RELOAD 20;

'-5D.0D 0.00 l/OLUMETRrC

50.00 STRRIN

100.00 MICRO-

150.00 200.00 STRRFNSCXID**!)

250.00

A-25

►WMIMWUI—Hffi'llW»»«

ü o o M

O o

TEST NUMBER "21 DmiiEfER IQ IN CDNffNING PRESSURE CHflRCDRL BLACK GR. i RKtflL SFRRIN 4 LflTERRL SFRfltN

5000 PSI (RELOAD 20>

-5 0.0 0 1 r-

0.00 5u.00 100.00 150.00 200 STRRIN MICRO-STRfl[NS(*lDfM)

oo 250.00

I I I I I I I i I I I I I !

I

A-26 r

6.00 MEAN STRESS KSI

8.0C 10.00 IQ.OD

A-27

£ o e*

1 ]

I TEST NUMBER 97 DIAMETER 12 IN m

» CONFINING PRESSURE 5000 PSI J ST CHflRCORL BLACK GRANITE

CO

co; iii i-

(

P1

>

Q

I I i

I

I "^ + I

a 1 1 1 1 1 1 ■ ^.00 10.00 20.00 30.00 «»sS.OO 50.00 60.00

SHEAR STRAIN MICRO-STRAINS<X10^2) |

A-28

1 1

■■■-^■■.-•■:::,::^,r;&W.Sv^:' ■ ■.■..., fev^:-^

M

M'

COe

«4 CO CO ÜJ Of h-c» CO«

ÜJ

ID

«. Ct

TEST NUMBER 37 OlflHETER 12 IN CONFINING PRESSURE 5000 PSI CHRRCORL BLACK GRANITE

T T 't.OO 10.00 20.00 30.00 40.00 50.00

VOLUMETRIC STRAIN MICRO-STRflINS<X10**2> 60.00

A-29

M

W

CO'

co; CO UJ

coi

X

<M

TEST NUMBER 9? DIAMETER 12 IN C0NFININ6 PRESSURE 5000 PSI CHRRCORL BL9CK GRANITE + RXIRL STRAIN A LATERAL STRAIN

-I- A

A+

T 1 1 1 1 I 10.00 0.00 10.00 20.00 30.00 40.00 50.00

STRAIN MICRO-STRflINS<X10^2>

A-30

0 C

mCliiNiiMNul ■ f

o

to-

o o

CM"

o o

CO

o CO 0. CO« Ixl

^—

o ct: o

i- GC

>

TEST NUMBER 2 0 DIAMETER 12 IN CONFINING PRESSURE 10000 CHflRCOflL BLACK GRANITE

PS I

o

Cvj

O o

-50 .00 0.0D 50.00 100.00 150,00 2D0 00

SHERR STRRIN MICR0-STRRINS(X10**1)

i 250 .00

A-31

o o

o CM

o IP

o o

m -

o IT1

TEST NUMBER 20 DlflMETER 12 EN CONFINING PRESSURE 10000 CHHRCDflL BLRCK GRRNITE

o

^o

LO LO ÜJ

I- o LO "V

z CE LaJ 21

a o

a

a o

-50.00 Q . 0 0

VOLUMETRIC 50.00 100.00 150.00 200.00

STRRIN MICRO-STRfl[NS(X10t+n

"■ i 250 .00

J 1 1 M

A-32 T

■w. mm

en

oo-

o o

O o

O' CO

^0

to- CO '-

CO LJ 01 h- o C0o

CM • _J - CE 1—4

X CE

o o CO

a o

o o

TEST NUMBER 20 DIAMETER 12 IN CONFINING PRESSURE 10000 CHflRCDRL BLACK GRANITE t AXIAL STRAIN + LATERAL STRAIN

PS I

-50 .00 O.OD 50.00 100.00 150.00 200 STRREN MfCRO-STRfllNSCXlO^l)

00 1

250 00

A-33

o o o-

o o in- CO

o o

en

o o in- <M

CO

o

UJ

o tt: ■

OS"1

LüS Q

o o in

o o

TEST NUMBER 2? DIAMETER 32 1(1 CONFINING PRESSURE 5000 PS I CHFIRCOflL BLACK GR - CYCLE ONE

**

^-lOO.OC -50.00 0.00 50.00 100.00 150.00 200.00 SHEAR STRRIN MICRO-STRfllNS(XlO^l)

A-34

rw»w^te^h.1.v,M;/-;v«;^i;i-.,*^->ra5^w^fi^*^'"::'i-'

■■■-*fmi^mmmfssm MiT)«twi.r.«wipmBBin-t»':i wr-'fltp"* Wt* t * ■■

O O

CM-

o o

,00.

o o

o o o

CO

in en ÜJ

co

2 (E ÜJ

o o CO

o o CM

o

00

o o :*■ i

o o

TEST NUMBER 27 DIAMETER - 32 IN CONFINING PRESSURE CHfiRCORL BLACK GR -

'5000 PSI CYCLE ONE

-»■ +

+

o, ] j , ^^ r_ , 1 1

0.00 2,5.00 50.00 75.00 100.00 125.00 150 00 VOLUMETRIC STRAIN MICRO-STRfllNSCXlO**!) '

A-35

o o

o o

o o o ■

o o

TEST NUMBER 27 DIAMETER 32 IN CONFINING PRESSURE CHflRCORL BLACK

+ RXIRL STRAIN

A LATERAL STRAIN

5000 PSI GR - CYCLE ONE

o ■

CO UJ <r \— o C0o

ITJ ■

_l ^ CE i—i

X (To

o

A 4 +

o o + +AA

+ A ^ A

+ A

o o

o

A -»A A +

50.00 -25.00 0.00 25.00 50 00 75 00 STRAIN MICRO-STRfiINS(X10*+l)

■—i 100.00

A-36

. ■ ■ .r- ■.:■.- ■ .-;- w .•■■,■-■:■■.■.:■■• .;■■■■ ■• ■ ■ ;■ ■ m ■ ■■ ■ • ■■ .■

Cl»

o O' •>»

o o »-

CO

o

co° LÜ or 1-

o a: • OS' »-• en

Q .

o

o o

TEST NUMBER 28 OlfVIETER 32 IN CONFINING PRESSURE CHRRCOHL BLACK 6R

5000 PSI CYCLE TWO

j 1 1 1 1 1 -100.00 -50.00 0.00 50.00 100.00 150.00

SHERR STRAIN MTCRO-STRRINS^XIO»*!;

—1 200.00

A-37

-:-■■■''■■•■■ :■.■■■■■-■■.<': :■-/■: .-■■■-■■■-:-'':?>■■■- ^ . i, , . ' '^ >,,. V ;

en

M

o o o

CO en ÜJ £o t— r» CO •

o o

TEST NUMBER 28 DIAMETER 32 IN CONFINING PRESSURE 5000 PSI CHflRCOflL BLRCK 6R - CYCLE THO

CC +

l-

+ I- +

I- + >

4 + + +

+ + + I-

+ 1 1 1 1 1 1

T).00 25.00 50.00 75.00 100.00 125.00 150.00

I

I I 1 I 1 I I I I I I I I I

VOLUMETRIC STRRIN MICRO-STRRINSCX10»*1> |

I A-38

:■- ■ ...

o-i

o o * 1

Kfmi

m

TEST NUMBER 28 DIAMETER 32 IN CONFINING PRESSURE 5000 PSI CHRRCOTL BLACK GR - CYCLE TWO

+ RXIRL STRAIN A LATERAL STRAIN

o o d-

o o •

* A

^L S

TRES

S K

SI

18. 0

0

20. 0

0 1

1

+

A

A A +

A +

A A + +

X o

A A h +

* A + + A

f A+ A

o •f f A A •

ir» 1- + A A f + A A

Al- A

o o + 4A A

+ A * • s t 1 I J —| '-50.00 -^5.00 0.00 25.00 50.00 75.00

STRniN MTCRO-STRflINS<X10*M) 100.00

\.

o-

Of

CO ^o o

COM UJ or 1-

o a: • OS- t- ec »—1

10

TEST NUMBER £9 DIAMETER 32 IN | CONFINING PRESSURE 10000 PSI S CHRRCORL BLACK GRANITE

I

3

++

^ 1 1 1 r 1 1 ^.00 10.00 20.00 30.00 40.00 50.00 60.00

SHERR STRRIN MICRO-STRfiINS<X10^2)

A-40

V

m

c*

€4

TEST NUMBER 29 DIAMETER 32 IN CONFINING PRESSURE 10000 PSI

gi CHflRCOflL BLACK GRANITE

COo "*• CO"

CO CO LU

£0 r—o CO • w

CC LÜ

+ +

+ + +

+ +

+ +

ci 1 1 1 1 1 1 Tl.00 10.00 20.00 30.00 40.00 50.00 60.00

VOLUMETRIC STRfilN MICRO-STRflINS<X10*»2)

A-41

. ■•v-^is«:,^::,..-«^ .^wm^i&jwmmm'y'*

TEST NUMBER 23 DIAMETER 32 IN CONFINING PRESSURE 10000 PSI

«H CHRRCOflL BLACK GRANITE

o o

CO + AXIAL STRAIN A LA1ERAL STRAIN

P»

CM

cog o-

O) LL) tt:

C0o

X (To

I I I I

I

A + A + AAA •*•

A m ^t* A« ■^

A + AA ++

A A* H M*

I

1 1 1 1 1 1 "-10.00 0.00 10.00 20.00 30.00 40.00 50.00

STRRIN MICRO-STRflINS(X10^2>

(j

PWWS ■-:... .■■..;

m

10-

CO

a C0o--| to« a: i-

o

OS"

i

10

TEST NUMBER 30 DIAMETER 32 IN CONFINING PRESSURE 10000 PSI CHflRCOflL BLACK GRANITE RELOAD

++ ++

+

+ 4*

d „ 1 1 1 1 1 " TJ.OO 10.00 20.00 30.00 40.00 50.00

SHEAR STRAIN MICRO-STRAINS<X10o#2> 60.00

A-43

■'■■-■■■■•.-■ ■■.■''-,.^-■- ■■■''■■•:'-'■■■>■■■■■;■■■■'■■ ■■'■r^Tt'vmyw^

TEST NUMBER 30 DIAMETER 32 IN CONFINING PRESSURE 10000 PSI CHRRCORL BLRCK 6RRNITE RELOAD

+ +

+ -»»■

+ +

a

+ + + ++ +

I- +

Q 1 1 1 1 1 1 ^).00 10.00 20.00 30.00 40.00 50.00 60.00

VOLUMETRIC STRAIN MICRO-STRflINS<X10^2)

I !

I I 1 I I

A-44

I I I I 1 I I I

■ ■ ■■ ■ iV'f ■■■ ■ - •■ :. ,, ■■

o o ID" m

o o •

cog

CO UJ a: C0o

x GCo

TEST NUMBER 30 DIAMETER 32 IN CONFINING PRESSURE 10000 PSI CHftRCORL BLACK GRANITE RELOAD + AXIAL STRAIN A LATERAL STRAIN

1 i i A

i A

L

4 + A

4 A

, , , , ,

MO.00 0.00 10.00 20.00 30.00 40.00 STRAIN MICRO-STRflINS<X10^2)

—1 50.00

A-45

■■"-'■■■■• "'-•:" m • ■■ m■■'• •■• i■ ''--^MgwMwwitiwisMwwi^^ ,

t*

O O

TO

CO ^o

o

CAS UJ a:

o

PS"

Q .

ID

TEST NUMBER 31 DIflMETER 32 IN C0NFIN1NC i PRESSURE 6050 PSI CHRRCORL BLACK GR ~UNIflXIfll£ E

+ f

+

■

+

»■

+ •

+ +

+ + +

^ + f

+ f \

+ f + +

+ + + f

+ + +* + + + +

h + f + + f + +

+ + + + f

\ +

+ + f + + s _____ i I 1 1 1 1 1 -10.00 0.00 10.00 20.00 30.00 40.00 SO .00

SHERR STRAIN MICRO-STRflINS<X10**2>

A-A6

. .*;;.,.. ^«naßaim^^mmm ■ :■■■- »a, , ■...; ■.

lo- co

cn

10-

COo

CO CO ÜJ

TEST NUMBER 31 OIRMETER 32 IN CONFINING PRESSURE 6050 PSI CHfiRCOflL BLACK GR -UNIRXIRL E

ill

o

+

+ +

+ +

+ + +

+ + 4

+

+ ♦

+ 4 4 4 f

f 4 T T T T

'-10.00 0.00 10.00 20.00 30.00 40.00 VOLUMETRIC STRRIN MICRO-STRfllNSaiO^;»

—1 50.00

A-47

, xmmrma^mmKVtmn^mmmmmmmmim0iimmmii<f^^

TEST NUHBER 31 DIAMETER 32 IN

. CONFINING PRESSURE 6050 PSI »H CHRRCORL BLRCK 6R -UNIRXIRL E CO

V*

ttt-

o- to« cn or So

ID-

i—• X (To

r. i i

4. RXIRL STRRIN A LRTERRL STRAIN |

A A A

f

A A

A+*

AA

A +

A » + +

* 1 A + *• f +

A ^ A h + + +

A A A + + + +

4 1 A •♦• + +4

A ^ A + + * +

A AA A f + + f

A * A + +

H-

A AA A ► •»■ + +

A M ♦++ ♦

A AA f ♦ f •f

A A f ♦ Af

♦ A ^ ++•- A

♦ A4 A +

A

1 1 1 1 1 1 '-10.00 0.00 10.00 20.00 30.00 40.00 50.00

STRRIN MICRO-STRRINS<X10♦♦a >

A-48

'■■■■■■'•■ '-^ ' ...,,, ,, .

■ ■ .

o

oo

C3

n a

-I

TL^T Ml'MBtR 2'4

DlflflLFLR 2 .00 TN LQNFININf-, PRtSSURL

D.OHR CITY TONRLITt

5000 PSf

"I

'Jl

fO ^ LÜ CK y

CO I

or "j

t '

n a -I

'1

I fJ . 0 Ü 0 .00

SHERR

—i 10 .00

TRRIN

T

20.00

MICRO 30 .00

STRFilN? MO .00

^ X 1 0 ♦ ♦ 2

—i 50 .00

A-49

CD

'-J

r ■»

rn r. N<' ;

if) '/' LL! (X

'/I c>

y cr

ri

rj C3

'E^T NUMBtR 2M DTflMLTLR 2.00 TN

CONfTNING PRL"SURt CEDRR CITY TÜNFILITL

500Q PS[

T 1 -10.00 0.00 10.00 20.00 30.00 '♦0.00 50.00

VOLUMETRIC STRRIN MICRO-STRRJNSCX10**2)

A-50

I I

CO

o

CO

vS CD ■*■ cn Ixl Qd \—

_)"•' a: x

CJ

o CO

TEST NUMBER 24

DlflMETER 2.00 [N CONFINING PRESSURE

CEDAR CITY TONAL ITE + AXIAL STRAIN

♦ LATERAL STRAIN

5 0 00 PS I

i 1 r 10.00 0.00 10.00 20.00 30.00 MO

STRRtN MrCRO-STRRINS(X10^2) oo 50 .00

A-51

wrarmvttnf^mx.mtf&m.mnem-rf&iminnwirr Kwwrwnv****" ■

o o

oo CM

I I I I

CM

o CM

CO

CD

CO-• LÜ

i— CO

OB-

TEST NUMBER DlflMETER 2.00 IN (ÜNFFNING PRESSURE CEDAR crr^r TONAL ITE

5000 PSI

o

en ■—i

>

o

-10.00 0.00 SHERR

lo.oo 2o.oo 30.00 qo 00

STRRIN MICRO-STRRINS(X10^2) 50.00

A-52

I I

o

C3

C3 in

C3 o

<N

CO ci

CO «n

LÜ

CI

to in

TL5r NUMBtR 25 ÜlflMLFLR 2.0Ü IN CDNFININb PRESSURE ChCll'lR Cin TONRLITE

5000 PSI

10.00 (J.OO

VÜLUMtFRIC

i 10 .00

SIHR IN

! r

20.00 10.00

MICRO-STRniN: H0 .00 50 00

A-53

IT)

CJ

O m

CD

in CM

CO o

o en ~ CO Ld OH \— a CO a

m _l - CE

X CEo

o

Q C3

O o

NUMBEj

CONFININy PRESSURE CEGflR CIJI TONAL ITE + ajpflL STRAIN

.ATERAL STRAIN

5000

-10 .CO 1 T r

0.00 10.00 20.00 30.00 40 STRAIN M[CRO-STRRINS(X10^2)

oo —i 50.00

A-54

KPWBSI^'-^i^M. *!**-—^^ -■ ■

W^lfM'miammmmmmmmmmmtiwnmrmm--

Sl

OJ-

o CO 0. (/) « UJ a: h-

o

>

Do

OJ

l£5r NUMBER 9€ DIRMErCR 2.OQ (N CONFINING PRESSURE 10000 PSI CEDAR C(n rONflLlTE

10.00 0.00

SHERR 10.00

STRRIN

1 1 1 1 20.00 30.00 HH.SO 50.00

MICRO-STRRINSCXIO^?:)

A-55

Q

O O

Q Q

O O

O -

Ul o

U) U) LiJ tt:

z CE ÜJ E.

V«

o a

a o

TEST NUMBER DIAMETER 2.00 CDNfIN1NG CEDAR CITY TONAt

I I I I 1 1 1 I I I I

-ID.DO 0.00 1000 20.00 30.00 HO.00 VOLUMETRIC STRRIN MICRD-STRFKNSCXIO^?)

50.00

A-:>6

I i I I I I

mimmmmmmmmmmmmm** ..■■.«,„.„,

o «>■

o tsi-

o o o-i

V)

CO00

CO Lü

CO CO

X cn

Csj

TEST NUMBER 2G oinriErER 2.00 IN

CDNfINING PRESSURE CEDAR CITY TONAL ITE ■< AXIAL STRAIN 1 LATERAL STRAIN

10000 PSI

T '-10.00 0.00 10.00 2D.00 30:00 40

STRRCN M[CRO-SrRfl[NS(X10t*2) .00 ,50,00

O: • I

CD

i O o

• 2 o I o

•

I 1 TEST NUMBER 33

o o

DIflMETER £ IN CONFINING PRESSURE 15000 PSI+ I CEDAR CITY TONfiLITE +

»-< + I

Sd +

+ I &i- + LÜ + a: + I Wo •f

o fli- ps

+ I H C 4 t-4

>_ + I

DE

16.

OQ

1 i

o I oj

• OP +++

++ +++

I o^ |» I .«

r3 ,

00 25.00 i

50.00 75.00 100.00 125.00 150.08 A

SHEAR fTRfllN MICRO~STRflINSCX10#*2) 1 I

A-58 f

CO

TEST NUMBER 33 DIAMETER 2 IN

A C0NFININ6 PRESSURE 15000 PSI gH CEDAR CITY TONflLITE

A + RXIflL STRfllN* A A LflTERRL STWWN A Ä + A +

A + A +

A + A +

a

+ o'H A +

A +

COg A 4-

toTO - -+

0) ÜJ a: (0°

IM

X (Co

»-

A 4

A -f-

% #+ A -H-

v

o o

44^'

s 1 1 1 1 1 •-£5.00 0.00 25.00 50.00 75.00 100.00 125.00

STRfilN MICRO-STRflINS<X104*2)

A-59

•■' • s ■»■mmmmarmwmi:-mm.&*i*m

O

o- M

O

IO-

o

a: i-

>

Qo to

TEST NUMBER 95 DIAMETER 4 IN CONFINING PRESSURE CEDRR CITY TONflLlTE

f*

5000 PSI + +

* +

+ +

+ +

^00 H-HH 1 1 1 1

10.00 20.00 30.00 40.00 50.00 SHEAR STRRIN MICRO-STRflINSCX10^2)

i 60.00

a 1

»-1

TEST NUMBER 35 OTRMETER 4 IN CONFINING PRESSURE 5000 PSI CEIMR Cm TONflLITE

„„.w« ^v.wu »ü.OO 50.00 60.00 VOLUMETRIC STRAIN MICRO-STRflINS<X10**2)

O IT»

^ TEST NUMBER 35 +

OinnETER 4 IN A CONFINING PRESSURE + 5000 PSI

^H ^ CEDAR CITY TONRLlTE* + RXlflL STRRIN A LATERAL STRAIN+

it»

+ + ♦

cog o-

CO" CO UI (Z \- cos

CE I—I

X CE

M

4A +

A A +

m + +

«V + +

* A ^

^r—i ^ , , , j

-10.00 0.00 10.00 20.00 30.00 40.00 50.00 STRfiIN MICRO-STRflINS<X10♦♦£)

A-62 1

e

to

ID

TEST NUMBER 36 OlflHETER 4 IN CONFINING PRESSURE 5000 PSI CEDAR CITY TONRLITE

CO

o

CO» UJ

o

♦ 4-

+ +

f +

cL*-■ •r—' 1 1 1 1 1 D.OO 25.00 50.00 75.00 100.00 125.00 150.00

SHERR STRAIN MICRO-STRniNSCX10^2)

A-63

oi-

C4

Of

COc

CO CO bJ

*— o CO •

UJ

4f •»■ +f +

+n+

I I I I I I I I I I I

^ I I I

TEST NUMBER 36 OMMETER 4 IN CONFINING PRESSURE 5000 PSI CEDAR CITY TONRLITE

+ + + +

+

+++ s j+t ^_______ f a. . ' 1 1 1 1 1 I TJ.00 25.00 50.00 75.00 100.00 125.00 150.00

VOLUMETRIC STRAIN MICRO-STRflINSCX10*#2) •

1 A-64

I

:'-3L- '■-jB^sflM^r'^v rrrwmm*

to

to to

cos

CO*1»

111

»-2 CO« *•

icsi

X (To

o

o 00

TEST NUMBER 36 DIAMETER 4 IN CONFINING PRESSURE CEDAR CITY TONALITE + AXIAL STRAIN A LATERAL STRAIN

+ +

+

Z

5000 PSI

T T T T '-25.00 0.00 25.00 50.00 75.00 100.00

STRRIN MlCRO-STRflINS(X10^2) 125.00

A-h

o

a

US I

n C)

:H

er i V 1

CO « , UJ ;

t \ 0

rr = J

-I

CD

o

TLST NUMBER 16 DlPilETER 1 [N CONFINING PRESSURE 1000D LEDRR CITY TONAL ITE

PSf

-10 .00 1 1 1 1

0.00 10.00 20.00 30.00 40.00 SHERR STRRIN MICRO-STRRINS(X10**2)

50.00

I I I I I i I I i I I I I i I I

A-66

1 1

a

o o

;tsr NUMBER 119 OrflliETER M li CONFfNrNG PRESSJRE 10000 PSf CEDAR Cm TONflOTC

-ID.00 0.00 VOLUMEFREC

10.00 STRRIN

20.00 30.00 ^0 00 MICRO-STRflINS a 10 t ^2)

50 .00

o a

II

o

T

a

If) 00

m UJ

\~- ^S

a: i—<

x en

a o

o

Q

I I I I I

I I

TEST NUMBER 18 DIAMETER 4 [N CONFINING PRESSURE 10D00 CEDAR Cm TONAL ITE + AXIAL STRAIN ♦ LATERAL STRAI4

PSI

-10.00 1 1 1

0.00 10.00 20.00 30.00 40.00 STRniN MICR0-STRRINS(X1Q^2)

50.00

A-A A

i I I I I I I

'mmmmmmm^mmmm^msfm^m^mm'^^^ mmm^f'v:■:-■■':■-■■■■■-'-■■■: ■ --■-::■

a

o

o in

o in

CM-

CO

a

CO- LL' DU \- co

Q^° 1 o^- I- CE

Qa in

o in

TtSr MUMBER DIRflETER 4 IN l

CONMNINb PRESSURE CEDRR CIT>f TONAL TTE

15000

-10.00 0.00 10.00 20.00 30.00 ,40.00 SHERR STRRIN M IGRO-STRRINS-CX 1 0 ♦♦2 )

50.00

CM m

CD en

CO M

:J

o C3 1

CD

a ID a

cn UJ

i— a

C/) • CM ■—i z a:

UJ

o o

o

o

TEc:;r NUMBER 22 FIMETtR q [N

CONFINING PRESSURE

CEDAR CITY TONFtlTE

I I

15DD0 PSI

I

10.00 0.00 VOLUMETRIC

"i 1 r 10.OD 20.00 30.00 40.00

STRAIN MICRO-STRRINS(X10**2) 50 .00

I I I I

A-70 I

'^WI^PSW^WjSfSaSSK.*.' mmmmmmnaa^mmmm^ni,^-,--.-,:'^,^',-, .v. .

o ! C3 i

c-j

er ei 1

V ;:3

f.j -i X -x'

rr. i.J V

i r.i ! C/.i

n ; ITi —

J er

•-• ,

i ..-i

K i

(T C3 i

=i -

NUMBER WETER 1 [N

:0NFINING PRESSURE CEDAR CITY TONAL ITt ■i FIX I AL STRAIN

♦ LATERAL STRAIN

150D0

lü.'JO Q.QQ

STRREN

1 1 10.00 20.00 30.00

MrCRd-STRRINSCXlO^ M0 .00

""I 50 .00

"2 )

A-71

Q O

(VJ

OJ

10.DO 0.00

SHEAR 10.00

STRRIN 20.00 30.00 40.00

M[CRD-SrRR[NS(XlD**2) 50 .00

I I I I 1 I I I I I I I i I I I 1 I

A-72

.■-'* r .■;.;:,■■ .■-..■■-,■■ .;.. ^ ■:■;,.,.-,...:-.l ..:,..,:-,

CM- CO

00- CSI

O O

■3—

O O

CM

0)0

TEST NUMBER TQJ DIRMETER 1.0 0 N CONFINTNG PRESS JR£ IJBÖfi PS I

CEDRR ctn roNRtrrE

a>-

CO ÜJ

^: CO csi-

CE ÜJ

o o

oo

1 , r

-10.00 0.00 10.00 20.00 30.00 HO.00 VOLUMETRfC STRflCN M[CR0-STRRINSCX10**2)

i 50.00

A-73

o a

VA

O o

in

o a eo-

o a

CM-

(J) LÜ m

T-

a: 1—4

X CEo

u> -

a o

»ER IR 4. DO [N

IING PRESSURE CIT'f TONAL IFE

'+ AXIAL SfRRCN ♦ LflTERRL SfRRCN

15000 PSI

10.DO 1 1 1 1

0.00 ID.DO 20.00 30.00 40.00 SrRR[N M[CRO-STRRINSCX10^2)

50.00

A-74

I I I I I I I i I I I 1 1

a

.1 r- i

o

r3

CJ I

ÜJ a: ^-

^ i of o J

■H

i— CE i—i

>

o.-

o

H

^3 •a

TEST NUM3ER DlfllETC,; 12 tN CQNriNING PRESSURE 5000 CEDRR CIT't TQNRLITE

-10.00 0.00 10.00 20.00 30.00 HO.00 SHERR STRRIN MICR0-3TRRINS(X I 0♦♦2)

—i 50 .00

A-75

MMms

I*

a

T ■

CD

t.»

a o

TESr NU^E"? 17 aiariETER 12 IN

CONFINING PRESSURE 500D CEOflR CT^Y TONRLITE

PSI

CD

■x Ixl

I- o

KB z: T U.I

a o

•IC.QQ 0.00

VOLUMETRIC 10.00 20.00 30.00 40.00

STRAIN MICRO-STRRINSCX10**2) 50 00

A-76

o C3

CO n

CM-

CD

CO CO ÜJ ct: »— CO

J u»

X CE

NUMBER

Y TONAL: IflL STRAIN TERAL STRAIi

00 PSt

10.00 0.00 10.00 20.00 30.00 40

STRRLN M[CRO-STRRINS(X10+*2) oo

—i 50 .00

A-77

<M

O

»I

to

ei-

(0

LJ

h-

>

Qo

TEST NUMBER 38 DIAMETER 12 IN CONFINING PRESSURE 10000 PSI CEOflR CITY TONALITE

ID

©I

+

f

+

1 1 1 1 1 9-25.00 0.00 25.00 50.00 75.00 100.00 125.00

SHEAR STRAIN MICRO-STRAINS(X10^2)

A-78

ei

ID

04"

COS

CO CO ill

l-o CO».

CC UJ

o o

• to

Ci

TEST NUMBER 38 OIRHETER 12 IN C0NF7.NTNG PRESSURE 10000 PSI CEDftSI CITY TONfiLITE

+ +

+ + + •f

+ f

\ + +

+ +

+ ++ 4

+ +

+

'-25.00 0.00 25.00 50.00 75.00 100.00 125.00 VOLUMETRIC STRfilN MICRO-STRflINSCX10**2)

A-79

«n

!«»■

to

ci-\

$2 o-

CO UJ

»—• X

to

en

TEST NUMBER 38 OIRHETER 12 IN CONFINING PRESSURE 10000 PSI CEORR CITY TONRLITE + RXIRL STRRIN A LRTERRL STRRIN

A +

A +

%4m

+A+A

1 o 1 1 1 r 1 1 -25.00 0.00 25.00 50.00 75.00 100.00 125.00

STRAIN MICRO-STRRINS<X10^2)

A-80

;^wä(^:'^**-**^»£-£*w^ ■.■■)■■ --■■■■ il--

o

It»

5-"

»'

iO

oi-

TEST NUMBER 32 DIflHEIER ^2 IN CONFINING PRESSURE 3510 PSI

CEDriR CITY FüNfiLlTE - UNflXIflL

CO

o C0o-. coS Lü

♦-

o

> Wo Qo

+

+

o iO

4 ■ff

+

D- i r— 1 —i 1 -25.00 0.00 25.00 50.00 75.00 100.00

SHERR STRRIN MICRO-STRRINS<X10*»2) 125.00

A-81

ai

o ID

mi

O O

CM-

CO o

CO CO LJ a:

en u

o o

o ID

CM

TEST NUMBER 32 OlfiMETER 22 IN CONFINING PRESSURE 3510 PSI

CEDAR CITY TONflLITE - UNflXlfiL

+ +

+ +

+

+ ++

E I I

I I

-25.00 0.00 P5.00 50.00 75.00 100.00 125 00 ■ VOLUMETRIC STRAIN MICRO-STRfiINSCX10^2) ■

I A-82 |

o •

CM

A +

o

A +

TEST NUMBER 32 DIAMETER 22 IN CONFINING PRESSURE 3510 PSI CEDAR CITY TONflLITE - UNAXIflL

+ RXIflL STRAIN A LATERAL STRAIN

a o

o to CM-

*° o-

CO ÜJ or »-

cr »—< X a:

o o If»

o

CM

o o

-25.00

A +

A +

A+ A +

^+*

A +

A + A +

A+ Af A+

A "I T T T T 0.00 25.00 50.00 75.00 100.00 STRRIN MICRO-STRRINS(X10**?)

125.00

A-8<

DASA 2698 July 1971 UNCLASSIFIED TRIAXIAL TESTS ON LARGE ... · Principal Investigator and Madan M....

Documents

Transcript of DASA 2698 July 1971 UNCLASSIFIED TRIAXIAL TESTS ON LARGE ... · Principal Investigator and Madan M....