o ID

-aj IITRI Project No. D6059

Semi-Annual Technical Report

EFFECT OF SPECIMEN SIZE ON CONFINED COMPRESSION TESTING OF ROCK CORES

for

Bureau of Mines Twin Cities, Minnesota

July 1971

Roproducod by

NATIONAL TECHNICAL INFORMATION SERVICE

Spnrmtiold Va 22151

IITRI Project No. D6059

Semi-Annual Technical Report

EFFECT OF SPECIMEN SIZE ON CONFINED COMPRESSION TESTING OF ROCK CORES

for

Bureau of Mines Twin Cities, Minnesota

July 1971

D D C lnp^rn ffl

C

IIT RESEARCH INSTITUTE Technology Center

Chicago, Illinois 60616

IITRI Project No. D6059

Semi-Annual Technical Report

EFFECT OF SPECIMEN SIZE ON CONFINED

COMPRESSION TESTING OF ROCK CORES

by

Peter Jay Huck Madan M. Singh

Monitored by

Bureau of Mines U. S. Department of the Interior

Twin Cities, Minnesota

Sponsored by

Advanced Research Projects Agency Washington, D.C.

July 1971

>D D C^

SEP tZ 1971

ESEITU'El c

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, Bureau of Mines, or the U. S. Government.

" Dir-TRIEUTION STATEMENT A f __._ i— <' ?'

Approved hr public releotM}

FOREWORD

This is the semi-ar.nual report on IIT Research Institute

(IITRI) Project No. D6059, entitled, "Effect of Specimen Size

on Confined Compressicn Testing of Rock Cores" co ;=ring the

work period 29 December 1970 to 15 July 1971. This program is

being performed under Contract No. H02100Ö9 with the Bureau

of Mines of the U. S. Department of the Interior, with Mr. Egons

R. Podnieks of the Twin Cities Mining Research Center acting

as technical monitor. The program is being spenscred by the

Advanced Research Projects Agency of the U. S. Department of

Defense under ARPA order no. 1579, Amendment 2.

The project is being conducted jr.der the direct s ;per

vision of Dr. Madan M. Singh, who is tcrvlng as pcrgram manager,

Mr. Peter J. Huck is project engineer. Othsr TITRI staff

members contributing to the overall research effort include

Drs. R. H. Cornish and A. Semmelink; and Messrs. L, A, Finlaysc

P. A. Hettich, E. J„ Smithy J. Vosatka a-d A Wa^r iz -

Respettf-'.l s r-nr.ltted

IIT RESEARCH INSTIT' TE

Madan M. Si->- M.» v r Soil a-d Re. K Mi : .A U I

APPROVED:

HO»* R. H. Cornish Director of Research Mechanics of Materials Di rltic:

MMS/bk

IIT RESEARCH INSTITUTE

i

IITRI PROJECT NO. D6059

Semi-Annual Technical Report

(Covering the Period 29 December 1970 to 31 July 1970)

Sponsored by

Advanced Research Projects Agency

ARPA Order No.;

Program Code Number;

Contract No.;

Title of Work;

Name of Contractor;

Effective Date of Contract;

Contract Expiration Date;

Amount of Contract;

Principal Investigator and Phone No.;

Project Engineer and Phone No.;

ARPA 1579, Amendment 2

1F10

H0210009

Effect of Specimen Size on Confined Compression Testing of Rock Cores

IIT Research Institute 10 West 35th Street Chicago, Illinois 60616

29 December 1970

29 January 1972

$75,791

Madan M. Singh AC312/225-9630 Ext 4784, 4785

Peter J. Huck AC312/225-9630 Ext 4735

Experimental Apparatus

Four sizes of rock cores are to be Investigated In this

program. Each core size was tested In a different pressure

cell. The specimen dimensions and pertinent pressure chamber

specifications are listed below:

IIT RESEARCH INSTITUTE

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Specimen Dia.(in.)

Specimen Length(in.)

Chamber I.D.(in.)

Chamber Pressure Rating(ksi)

Maximum Rated Axial Load(lb.)

2.06 4 4.0 30 375,000

3.65 7 6.5 30 995,000

12 24 14.7 20 3,400,000

32 or 36 60 48.3 20 axial 10 confining

36,500,000

To date only two (2) 2-in. diameter specimens have been subjected

to triaxial pressure. The other cores have already been prepared

and gaged. The apparatus for the tests has also been set up.

The test data should become available in the near future.

Prior to testing the rock cores triaxially, the

cylindrical specimens were tested acoustically to map out any

major variations in acoustic velocity through them.

Triaxial Cells

Each triaxial cell consists of a thick-walled pressure

chamber with a honed interior in which a floating piston moves.

A typical arrangement is depicted in Figure 1. The triaxial

cell for the 2-in. dia. specimens carries a spherical seat

between the piston and the specimen. Because of size restrictions,

spherical seats are not used in the larger specimens. Instead,

all pistons are provided with special high compliance seal rings

that allow the pistons to rotate to conform to the rock specimens.

A capping platen covers the top of the core, with a chamber closure

above it to hold the assembly in place. The strain gage leads

from the rock core and are led through this closure to the data

acquisition system. The confining pressure is introduced around

the jacketed core, while the axial load is applied by pumping

oil below the sliding piston. This scheme for applying axial

pressure eliminates the need for a large separate loading machine,

and can withstand fairly high loads, depending on pressure cell

design.

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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

The 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:

a2 - 03 - P3

At ^1 - (prp3) xl 0]_ - Ö3 + AOj^

where»

A_ - piston area P A - specimen area

P, ■ axial chamber pressure

Po ■ confining chamber pressure

Aa. ■ deviator stress

a,, 02 and Q« - principal stresses.

Reference to Fig. 1 and the above equations confirms that

if P, - P«, Ao- - 0 and the specimen is under hydrostatic

stress (a, - a« ■ o^). For P« - 0, the specimen is unconfined,

with Oj - a3 - 0 and «^ - ^a^ - p^^ A /Ar.

The 4 in., 6 in., and 14 in. dia. pressure chambers

are incorporated into a central control panel and instrumentation

system and are operated by a common pumping system. A schematic

of this layout is given in Fig. 2.

In each of the tests to be performed in this program

the rock core is loaded hydrostatically up to the predetermined

confining pressure, and then the axial pressure is increased

gradually to the desired value. It is planned to run at least

one load-unload-reload cycle on each specimen. During the

reload the axial stress is increased until the core fails or

the capacity of the cell is attained, whichever is lower.

NT RESEARCH INSTITUTE

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5

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Cross-connections have been provided between the confining

and axial pressure sections of the cells, to obtain true

hydrostatic loading during the hydrostatic phase of each

experiment.

Large Pressure Chamber

Because of the unique design of the 48-In. diameter

pressure vessel, it deserves separate discussion in this

report. Detailed descriptions of the design and chamber may 12 be found elsewhere ' . A schematic of the vessel layout is

depicted in Figure 3, and a photograph of it is shown in

Figure 4. Essentially the vessel is comprised of a 48-in.

I.D., 86-in. working length hollow cylinder capable of with-

standing 20,000 psi internal static pressure. The ends of

this hollow chamber can be closed with steel plugs, which

react against a flexible frame built up of strap steel. The

cylindrical chamber walls consist of 12-in. long, 13 1/2 in. thick

steel rings, placed end to end and held together by a single

3/4 in. thick steel liner along the inside diameter. The

reaction structure consists of a basic frame held together by

steel strap wrapped around it. The entire vessel weighs

140 tons, which is substantially less than conventionally

designed chambers having the same capabilities. The cell can

withstand axial loads of over 36 x 10 lb.

The pumping and control systems for this unit are

simpler than those for the smaller chambers. A separate

pump is used at each end of the chamber, as is seen in the

schematic in Figure 5. Accumulators are 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 is on the order of a week Instead of an hour. The

tests in this chamber differed slightly from those in the IIT RESEARCH INSTITUTE

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Details of illustrations in this document may be better

I Ftg. 4 PHOTOGRAPH OF 48" PRESSURE CHAMBER

8

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a

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r smaller test cells. In order to maintain seal Integrity, a

positive pressure differential of about 200 psl will be maintained

across the sliding piston during the "hydrostatic" portions

of the trlaxlal tests, and the axial pressure will not be allowed

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

cycle. If the&e precautions are not taken, there would have

been danger of upsetting the piston seal, thus aborting the

remainder of the test.

Specimen Reparation

The 12-In. and 32-in. dla. cores of Charcoal Black

gvanlte were obtained from the Cold Spring Granite Company,

Cold Spring, Minnesota, and the 12-lno and 36-in. dla. specimens

of Indiana limestone were ordered from Rechal Stone Co., Glen-

view, Illinois. These specimens required no further preparation.

Extra rock was ordered with each of the two types, so as to

permit coring of the 2-in. and 4-in. dla. specimens. The smaller

cores were cut parallel to the axis of the larger cores so as

not to Introduce complications due to anlsotropy. One direction

along all the cores of Indiana limestone were marked at the

quarry. It was also marked on the cores drilled In the laboratory.

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 will be capped in

a specimen cage to permit handling. The capping material tc be

used Is a steel-filled epoxy. 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 roads corresponds to 30 psl compressIce stress in

the rock specimen, the effect of the cage on the rock will

be negligible.

An airay of foil strain gages have been mounted on each

specimen. The number used ranged from three resettes on the

2-ln. cores to thirty rosettes on the 32-ln. cores. These were

lir RISEARCH INSTITUTE

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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

JL,

visually inspect for voids in the cement

base

it affix and wire gages

apply two coats of gage cement for water proofing

check gage for continuity and response (soft eraser) and replace if necessary.

The instrumented cores will be waterproofed with latex

cement over the foil gages, and at least two coats of latex

paint with a thickening agent 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 can not be loaded to failure

on the second load cycle, the specimen will be recovered

intact and stripped of paint for visual inspection.

Instrumentation and Data Reduction

The foil strain gage on the rock specimen provide the

mechanical properties information required in this project.

These gages are driven by a bank of bridge balance units, wired

to provide temperature and pressure compensation for the leads.

Temperature gages are provided in the chamber adjacent to the

rock specimens to monitor environmental temperature. The data

are recorded by a Hewlett-Packard series 2012 data acquisition

system that scans all data channels on demand, printing the

IIT RESEARCH INSTITUTE

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voltages on paper tape. As the data system scans the strain

gages, the axial and confining pressures are read on Heise

bourdon gages, and these readings are manually Inserted on

the printed data system output.

Data reduction Is performed using lITRI's Unlvac 1108

computer. The printed data system output Is keypunched and

Input In an editing program. This program reads all the raw

data and prints It out In a convenient array for checking.

This program also plots the strain data so that any keypunching

errors or bad strain readings can easily be found and corrected,

After the data has been checked In Che editing program It Is

Input In an analysis program. This program solves the strain-

gage bridge equation Individually for each gage, and computes

the elastic moduli. The reduced data are printed out, and

the following computer plots are provided:

• devlator stress vs. shear strain

• volumetric stress vs. mean stress

• axial and radial strain vs. axial stress

• bulk, shear and elastic moduli vs. mean

stress.

These plots will be Included in an appendix to the final

report as the most meaningful and convenient method for

presenting the experimental data. Finally, the reduced stress

and strain data are punched by the computer to provide ready

access to the data for further analysis and model fitting.

Nondestructive Test Program

A series of nondestructive tests was planned for all

specimens in order to measure any anisotropy and to locate

any inhomogenelties in the larger specimens. These tests

Included Schmidt hammer. Shore scleroscope and dilatational

wave velocity. These tests are now complete with the exception

of the 12-in. dia granite specimens.

IIT RESEARCH INSTITUTE

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Schmidt Hammer

Schmidt hammer readings were taken at each gage

location, with the following exceptions. The 32-in. dia

and 36-in. dia cores were tested at every second gage location,

for a total of 18 tests on each core, and the 3-in. dia and

4-in. dia cores were tested on the ends only. The readings

on the small cores was strongly influenced by the boundary

conditions on the side of the specimen opposite the hammer

impact because of the small core diameter. After experimenting

with various seating and clamping arrangements, it was decided

to conduct these tests along the longest core dimension

available. Each Schmidt hammer test consisted of 8 readings,

the first 3 of which were discarded and the last b of which were averaged to give the Schmidt hammer value at that

location. This procedure is necessary because of local crushing

that occurs during the first few impacts at a point.

The Schmidt hammer data is summarized in Table 1.

Note that the values for the 2-in. dia cores is low in both

cases. This is attributed to the small specimen size,

rather than any actual difference in character. The numbers

in parenthesis are grand means excluding the 2-in. dia specimens,

and represent the best overall values for the two rock types.

Shore Scleroscope

The Shore scleroscope indicates hardness by the

measuring rebound of a small diamond tipped striker dropped

on the rock. A test consists of 10 readings taken near a

single point. The instrument is moved approximately 0.1 in.

between readings so the striker does not fall in the small

conical depression left by a previous reading. In granite,

the scleroscope reading depends strongly upon the type of

grain impacted. Tests were conducted near alternate gage

locations on the 12-in., 32-in., and 36-in. dia specimens,

and at all gage locations on the small cores. The results IIT RESEARCH INSTITUTE

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Table 1 SCHMIDT HAMMER SUMMARY

Indiana Limestone Charcoal Black Granite

Core Dla. Mean Number Mean Number

2 in. 24 24 35 14

! 4 in. 28 10 48 10 j

| 12 in. 28 90 - -

36 in. (32 in.) 30 54 50 54

1 All Specimens 28

(29)*

178

(154)

47

(49)

78

(64)

Parenthesis indicates 2 in. dia specimens exluded from mean.

IIT RESEARCH INSTITUTE

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are tabulated In Table 2. An Indication of the scatter Involved

Is shown in Figure 6, which is a histogram of the 54 individual

readings taken on the three 36-in. dia limestone specimens.

Acoustic Velocity Mapping

The velocity of the dilatational wave was measured at

all gage locations on all cores (with the exception of the 12-in.

dia cores which are not yet tested). The system used for the

small cores is shown in Fig. 7A. The input signal is a single

cycle square wave. This is amplified and used to drive a 1 MHz

piezoelectric transmitting transducer. The signal transmitted

through the rock is received by a similar transducer and displayed

on a dual beam oscilloscope through an internal variable delay

line. This signal is compared with the input signal, and the

variable delay line adjusted to achieve coincidence. The elapse

time is then read from the delay line. The system delay is easily

measured by removing the rock specimen and placing the transducers

face to face. Figure 7B shows the system used for the 32-in. and

36-in. dia cores. A mechanical delay line was introduced to allow

the use of rapid sweep rates, and a preamp boosted the received

signal. The operating frequency ranged from 300 kHz for the

large cores to 1 MHz for the small specimens. A check was made

to determine if the frequency response of the rock influenced

the apparent time of arrival by making measurements on a single

2-in. dia specimen at frequencies between 10 kHz and 2 MHz.

The results are plotted in Fig. 8, and indicate no variation in

time of arrival across the entire frequency range. The amplitude

of the received signal is, of course, strongly dependent on input

frequency.

The anisotropy of the Indiana limestone was investigated

by evaluating the three 36-in. dia cores. The 45 individual

acoustic velocity tests on these cores had a mean value of 4.021

km/sec, with 957. confidence levels at + 0.017 km/sec and a

standard deviation of 0.058 km/sec. This value of 4.021 +

MT RESEARCH INSTITUTE

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Table 2 SHORE SCLEROSCOPE SUMMARY

Indiana Limestcr.e. Chare:al B: .ack Granite

Core Dia. Hear. Nw.tr.:: er Mean Number

I 2 in. 12 36 6-* 21 1

| 4 in. 15 30 83 15

12 in. 14 45 - -

32 in. (36 In.) 14 54 75 54

All Specimens 14 165 74 90 |

IIT RESEARCH INSTITUTE

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Input Signal

Oscilloscope

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Fig. 7A ACOUSTIC VELOCITY SYSTEM FOR SMALL CORES

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0.017 km/sec is taken as the acoustic velocity in Indiana

limestone. These 45 readings may be separated into 3 groups

of 15 readings, each group spaced at 60 degree intervals

around the axis of the core, or as 5 groups of 9 readings,

each group spaced at 10 in. intervals down the length of the

core. In this fashion we can consider the variation in acoustic

velocity as a function of direction in the horizontal plane,

or as a function of the vertical depth in the bedding plane.

This nonemclature, and the variation of acoustic velocities as

a function of direction and depth are indicated in Figure 9.

Note that in all cases, the 95% confidence levels for the

individual subgroups include the mean value of 4.021 km/sec

computed for the entire 45 reading group.

Looking at the variation of acoustic velocity, it appears

that the maximum velocity would be measured along a diameter

between 2-5 and 3-6, along a quarry bearing of N-80o-W, and

the lowest velocity would lie along a bearing of N-10o-E. The

maximum variation is on the order of 1 1/2 percent of the mean

value. Considering the variation of acoustic velocity with

depth, there may exist a trend of increasing velocity with

depth. The slight reversal of this trend at row #5 may be a

real effect caused by the presence of the bedding plane in the

formation. In any case, the variation is on the order of 1%

or less. The acoustic velocities for all subgroups lie near

or within the 957« confidence levels for the entire group of

measurements.

Unconfined Compression Tests

Unconfined compression tests were conducted on three

specimens each of Indiana limestone and Charcoal Black

granite. These specimens were instrumented and the following

plots are included as an appendix to this report:

deviator stress vs. shear strain

mean stress vs. volumetric strain

NT RESEARCH INSTITUTE

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Specimen Orientation and Array of Measurement Locations

1 —

u

•2 3

2 —

I r 5 —

4

^4.05 r- I ^•4.00

•^3.95 >

4-—4- s -J -1 4.021 + 0. 017

T^ T? 3^ Direction of Measurement (column to column)

SU.05

4.021 + 0.017

<u >

12 3 4 5

Depth of Measurement (row number)

Fig. 9 ACOUSTIC VELOCITIES IN 36-IN. DIA INDIANA LIMESTONE

21

axial stress vs. axial and lateral strains

The failure stresses for the individual tests are indicated

in Table 3.

The orientation directions of the 32-in. dia and 12-in.

dia Charcoal Black granite cores were not marked by the quarry.

In all, 102 acoustic velocity determinations were made on the

2-in., 4-in. and 32-in. dia granite specimens These tests

had a mean value of 4.661 km/sec with 957» confidence levels

of + 0.047 km/sec with 95% confidence levels of + 0 047 km/sec

and a standard deviation of 0.240 km/sec. The value 4.661 +

0.047 km/sec is taken as the acoustic velocity in Charcoal

Black granite. Additional insight into anisotropy can be

gained by evaluating the acoustic data from the 2-in. dia

and 4-in. dia cores, which were cut at IITRI from a single

piece of granite, and were orientated with respect to an

arbitrary direction marked on the parent core. This evaluation

will be carried out in the future.

Triaxial Tests

Triaxial tests at confining pressures of 2000 psi

and 4000 psi were conducted on Indiana limestone. These

data have been keypunched, but not yet run on the data

reduction program.

NT RESEARCH INSTITUTE

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Table. 3 UNCONFINED COMPRESSIVE STRENGTH

Gran ita Limes tone

Test Failura Stress Test Failure Stress

14

15

17

17.4 ksi

23.1 ksi

18.2 ksi

20

21

22

4.18 ksi

4.38 ksi |

4.00 ksi

Mean 19.5 ksi Mean 4.19 ksi |

The data reduction for the unconfined tests is identical with that

which will be used for the triaxial tests.

MT RESEARCH INSTITUTE

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REFERENCES

1. Finlayson, L. A., Large Segmented High Pressure Chamber

Design, IITRI Internal Report dated March 4, 1970, p. 9.

2. Cornish, R. K. and Finlaysonj L. A., Reaction Frame for

Restraining High Loads, U. S. Patent No. 3,476,281,

Issued November 4, 1969, p. 4.

NT RESEARCH I JSTITUTE

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APPENDIX

Data from Unconfined Compression Tests

The plotted output for the six unconfined compression

tests is included or. the following pages. Each test includes

the following plots:

deviator stress vs. shear strain

mean stress vs. volumetric strain

axial stress vs. axial and lateral strains

The pertinent identification data are noted on each plot.

IIT RESEARCH INSTITUTE

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