Method for Unconsolidated-Undrained (UU) Triaxial

Compression Test on Rocks

1 . FOREWORD

This official standard presented by the Japanese Geotecbnical

Society (JGS) is for the unconsolidated-undrained (UU) triaxial

compression test methods on rocks. The original draft was

prepared by the Standardizing Committee of thc

Unconsolidated-Undrained (UIJ) Triaxial Compression Test on

Rocks (refer to Table I for the committee member

composition). Brief history and significance of this standard,

and notes are described in the following sections.

1 . I Brief history of the standard

To select laboratory and in-situ test methods to be

standardized, the Study Committee for the Rock Testing

Methods of the Japanese Geotechnical Society (chaired by

Professor Rymoshin Yoshinaka of Saitama University, founded

in 1993), conducted surveys on specifications and guidelines

officially used by both domestic and foreign academic societies

and organizations. The Couunittee studied practicability and

necessity of the new standards. Two-year study showed that

although the uniaxial and triaxial compression tests are widely

used and considered important, there are no standards covering

rock characteristics varying widely from soft to hard rocks. It

was therefore concluded that the establishment of a new

standard would be extremely importantl)

Under these circumstances, the Study Committee for the

Uniaxial and Triaxial Compression Test Methods on Rocks

(hereafter called the Study Committee), chaired by Professor

Yoshinaka, carried out a three-year preliminary investigation

since 1995 to collect and classify necessary infonnation for

standardization of the test methods. There werc five main

activities involved: ( 1) questionnaire survey; (2) nationwide

round robin tests; (3) literature research; (4) sorting out of

major points for standardization of test methods; and (5)

organizing symposiums focusing on the uniaxial and triaxial

compression test methods2)

The unconsolidated-undrained (UU) triaxial compression test

method on rocks presented here is based on the original plan by

the Standardizing Committee for the Triaxial Compression Test

Method on Rocks (founded in 1998). The draft standard was

prepared by the Standardizing Committee, taldng the results of

the study by the aforementioned Study Committee into

consideration, and presented on the monthly journal pf JGS,

Tsucld to J~so, Vol.47, N0.9_ This standard was then finalized,

incorporating the decisions reached through in-depth

discussions by the Study Committee for Standards Test and

Survey Methods on Rocks, and the Standardizing Department.

l.2 Significance of the specification

This standard for unconsolidated-undrained (UU) triaxial

compression test method is mainly for saturated rocks from soft

to hard rocks, and rock like geomaterials. Namely, the draft

standard is for test methods where a rock specimen is subjected

to a constant cell pressure in a triaxial cell, blocking the

Table I : Members of the Standardizing Committee for the Triaxial Compression Test Method on Rocks

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drainage path for pore water, while the axial stress is

monotonicauy increased until the specimen fails.

The aforementioned Study Committee conducted a

nationwide questionnaire to learn wbat sort of uniaxial and

triaxial compression tests on rocks have bcen conducted for

what purposes, and how the test results have been used.

Seventy-nine domestic organizations rcsponded (response rate:

65%) and multiple analyses on the survey results were

conducted3). Main results obtained so far are, as follows:

( 1) Next to the uniaxial compression test, the triaxial

comprcssion test is the second most important and

frequently used test method on sofi and hard rocks.

(2) Some of the commonly used triaxial compression test

methods for rccks are UU, CU (consolidated-undrained

test), CU (consolidated-undrained test with pore pressure

measurement), and CD (consolidated-drained test) methods.

For soft rocks UU, CU, and CD tests are used with a similar

frequency, whereas UU tests are much more frequently used

for hard rocks than CU, and CD tests.

The main reason to choose un as the test method for

standardization was because this UU method is the most

essential and popular one for both hard and soft rocks.

1.3 Outline of the draft standard

This standard comprises seven sections: 1. General rules to 7.

Re porting.

l.3.1 General

This drafi standard is "as a principle" applied to saturated

rocks and rock like geomaterials. The aforementioned

questionnaire showed that UU triaxial tests are frequently

conducted on partiahy saturated hard rock specimens. This is

why the phrase "as a principle" is used. The notes state, 'This

standard may be applied to partially saturated rocks". While

the unconsolidated-undrained (UU) triaxial compression test

method on soils (JGS 0521-2000) requires more than three

specimens, use of more than four specimens is recolmnended in

this standard_ This is because of the fact that rocks ajre

*'enerany less homogeneous compared with soils.

1.3.2 Test Apparatus

The UU triaxial compression test is frequently car:ied out to

determine design values and input data for stabnity analyses, as

well as to obtain appropriate strengths of rock masses and

inf;ormation necessary for rock mass classification. Reflccting

this, there are many cases where the uiaxial tests focus on

obtaining deformation characteristics along with strength

characteristics. 1'aking these trends into account,

"measurement of crrcumferential displacements" and

"measurement of longitudinal displacements on the sides of

specmens" are referred to m the notes. Accuracy required in

the measurement of longitudinal displacements is :!: 0.01'~o of

the specimen height.

1 .3.3 Preparation of specimens and measurement

The standard diameter of a specimen is set at 5.0cm and the

height is double the diameter. This is based on the results of

the aforementioned questiomaire, in which most organizations

responded with these dimensions- Although the notes with

respect to specimen dimensions state that "it is desirable to

make the diameter of specinen more than five times the

maximum rock grain", other dimensions may be more

appropriate for some rccks, such as conglomerate and rccks

consisting of coarse grains. This is fiuther explained in the

commentary section.

1.3_4 Setting of specimens

"3. Preparation of specimens and measurement" states

"specimens should be such that the both ends of specimens are

flat and unevemess is less than 0.02mm". However, some

rocks, such as poorly consolidated coarse sandstones never

meet this requirement. Capping is therefore referred to in the

notes.

1 .3.5 Test Method

The aforementioned questiomaire revealed that most

organizations are using either stroke-controlled or

strain-controlled tcst method. This is why this draft standard

requires a compression process where the specimen is

continuously compressed while keeping the longitudinal strain

rate constant. However, this standard may be applied to both

load-controlled and stress-controned test methods, since there

are organizations using these methods- In addition, taking

into consideration the necessity of the evaluation of Poisson's

ratio, the notes refer to the measurement devices for

circunferential displacement.

l.3.6 Evaluation of Test Results

Equations for calculating longitudinal strains and principal

stress differences are similar to thOse defined by the UU triaxial

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test method (JGS 0521-2000). In addition to these equations,

an equation for calculating the Poisson's ratio is given in the

notes.

1.3.7 Reporting

Considering the fact that tests are often conducted to obtain

defonnation characteristics of rocks along with strength

characteristics, the notes refer to the evaluation of deformation

characteristics. "Secant slope of the principal stress difference

vs. Iongitudinal strain curve at 50% of compressive strength"

(E*,50) and "Tangential slope of the principal stress difference vs.

longitudinal strain curve at 50% of compressive strength"

(E~50) are chosen as deformation moduli. Calculation method

for these moduli is explained in the commentary section.

Ref erences

l) Study Committee for Test Methods for Rocks:

Comprehensive Report on Test Methodsfor Rocks. Jap. Soc.

of Soil Mech. and Foundation Eng., 1995.

2) Study Committee for Uniaxial and Triaxial compression Test

Method for Rocks: Proc. of the Sym. on Uniarial and

Tria,~ial Compression Test Methods for Rocks and

Utilization of Test Results, Jap. Geotech. Soc., 1998.

3) Study Committee for Uniaxial and Triaxial compression Test

Method for Rocks: Report on Uniaxial and Triaxial

compression Test Method for Rocks, Jap. Geotech. Soc.,

1998.

2. JAPANESE GEOTECHNICAL STANDARD "METHOD

FOR UNCONSouDATED-UNDRAINED TRIAXIAL COMPRESSION TEST ON ROCKS"

Designation: JGS 253 1-2000

Method for Unconsolidated-Undrained Triaxial Compression

Test on Rocks

com pression.

1 ,2 Range of Application

This standard is mainly applicable to saturated rocks

and rock-like geomaterials.

1 .3 Defmition of Terms

UU means shearing rock specimens under und!ained

condition, without consolidating them (isotropically) prior

to shear.

Axial stress is applied in the longitudinal direction,

while lateral stress is applied in the radial direction of the

specimen. They are defmed at mid-height of the

specimen. The difference between the two stresses is

termed principal stress difference. Isotropic stress state

is defined as a stress state in which axial stress is identical

to lateral stress. Ceu pressure is the pressure applied in a

triaxial ceu. Lateral stress is equal to cell pressure.

Unconsolidated-undrained compressive strength of rock is

the maximum principal stress difference applicable to the

specimen without consolidation, and without letting pore

watcr move in and out of the specimen. Failure strain is

the axial strain when the maximum principal stress

difference is reached.

1. GENERAL

l . I Purpose of Test

The purpose of this test method is intended to obtain

strength and deformation properties of rocks, when

subjected to unconsolidated and un(kained triaxial

[Notes]

1 ,a. In case the method employed is partially different from this

standard, details shall be clearly stated in the report.

1 .b. Refer to the following speciflcations and standards for the

issues not defined in this standard:

JGS 2521: Method for Unconfined Compression Test on

Rocks

JGS 0542: Method for Undrained Cyclic Triaxial Test to

Determine Deformation Properties of Geomaterials

1.1a. Tests shau bc performed at diffierent isotropic stresses in

the required stress range, on as many specimens obtained

from the same material as required, usuauy not fewer than

four, to evaluate strength characteristics.

1 . Ib. This standard may be applicable to unsaturated rocks.

1 .3 This test may be abbreviated as "uo Triaxial Test on

Rocks."

2. APPARArUS

2.1 Triaxial Compression Apparatus

A triaxial compression apparatus consists of a triaxial

pressure chamber, cell pressure supply system, Ioading

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system, together with load and displacement measuring

devices. It shau satisfy the fouowing conditions:

( 1) Triaxial apparatus should bc able to sustain the maximum

axial compression load of the specimen and the maximum

ceu pressure.

(2) The apparatus should bc able to apply pressure

continuously to a specimen till the end of the test, with an

accuracy of :t 4kN/m2 for pressures less than 200kN/m2

and of :k: 2% for pressures greater than 200kN/m2.

(3) Axiai displacement or axial load should be continuously

applied at a constant rate of feed.

(4) Cell pressure should bc measured with an accuracy of :i:

2kN/m2 for pressures less than 200kN/m2, and of :!~ I %

for pressures greater than 200kN/ m2.

(5) Axial compression load should be measured with an

accuracy of :t l% of the maxiuum axial compression

load of the specimen.

(6) Axial displacement should be measured with an accuracy

of :~: 0.01 % of the specimen height.

(7) Loading cap and pedestal should be impermeable.

2.2 Misceuaneous Accessories

( 1) Specimen covering Inaterial

(2) Membrane stretcher

(3) Orings or rubber bands

(4) Specinen size measurement tools should be able to

measure the specimen height and diameter with an

accuracy of or better than O. Imm.

(5) Balance should be able to weigh the specimen to 0.0lg.

(6) Sample trinuning devices

[Notes]

2. Ia. A typical triaxial testing apparatus is mustrated in Figure

l . Schematic views of two different triaxial pressure

chambers are shown in Figures 2 and 3: Ioading piston and

loading cap are rigidly counected (Figure 2); and are

separated (Figure 3). In both types of the triaxial cens, the

specimen can be mounted between cap and pe(lestal with

the same diameter as tbat of the specimen. They are

covered with a rubbcr membrane, and sealed with O-rings.

b. Circunferential displacement, if required, should be

measured with an accuracy of 0.01% of the specimen

circumference.

( 1) Capacity of the cell pressure should be selected according

to the purpose of the test. In case the maximum axial

force is expected to bccome hrge, a loading frame with

high rigidity should be usedj so that the frame deformation

will not affect the axial displacement measurement.

(5) When a load cell is mounted outside the ttiaxial celL the

measured axial force should be corrected for frictional force

bctween loading piston and bushing. In case a load cell is

instaned inside the triaxial celL the effect of cell pressure

on the load ceu reading shouid bc calibratedj and correction

should be made for measured axial force.

(6) When the main objective of the test is to obtain deformation

proporties of rocks, the measurement of axial displacement

should bc made on the lateral suface of the specimen by a

proper technique.

(7) When there is a drainage hole or a porous disc is set in the

cap and/or in the pedestal, the drainage hole should be

closed off, using a ffat rigid disc with the same diameter as

that of the specimen.

2.2

( 1)a. Rubber membrane, heat sh:inkage tubing, or silicone

rubber may be used as specinen coveriug material.

b. Rubbcr membrane should be longer than the membrane

stretcher. The inner diameter of the membrane, when not

stretchedj should be in the order of 95% of the specimen

diameter. The thickness of the membrane should be about

0.25 to 1.0mm.

(2) Membrane stretcher should be cylindrical~ and its length

and inner diameter should be 5 to 10% larger tban the

height and the diameter of the specimen. The stretcher

should have a structure so that the rubbcr membrane can bc

stretched snugly against the imer side of the stretcher when

vacuum is applied. If the cap is rigidly connected to the

loading piston, it is desirable to use a membrane stretcher

that can be split longitudinally into two pieces. In this

case, the two pieces of the stretcher should be airtight when

assembled.

(3) The inner diameter of O-rings should be about 809i:o of the

diameter of the end cap or the pedestal where the O-rings

are put around, so that they have suffircient confiming force

to prevent pore water from leaking.

(4) Specimen diameter should bc measured by sliding calipers

or by Pi tape.

(6) Miter box, sample trimmer, straight edge, suface grinder,

diamond slab saw, and recoring devices are used for sample

trimming.

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air pressure

~~ regulator

¥:~0

ccll pressure

gauge

/

ceil

pressure fluid

Ioad celi

displacement

/ transducer

triaxial

pressure chambcr

specimen

loading frame

Figure I Typical configuration of

UU triaxial compression apparatus

loading piston

pressure cylinder

(acts as upper plate and

support column, too)

swivel

loading cap

specimen covering material

O-ring

u

loa

Ioc

defo

trans

specime

cen pressur

Ioadin iston

splacement

ransducer

loading cap

O-ring

specimen vering material

support column

pressure cylinder

pedestal

strain gauge

cell prcssure

line

Figure 2 Example of triaxial pressure chanibor in which

the loading piston is rigidly comected with the loading cap

up

specim

cell pres

line

n

is placement

transducer

loading cap

O-ring

specimen overing material

pressure cylinder

upport column

pedestal

Figure 3 Examples of triaxial pressure cha!Bber in which the loading piston is separate from the loading cap

(a) upper plate and support column are in one piece (b) pressure chainber is located inside support colunms

3. SAMPLE PREPARATION MEAS UREMENTS

AND SIZE

3. I Sample Shape and Sample Size

( l) Test specimens shall be right circular cylinders.

(2) Standard specimen diameter shall be set as 5cm.

(3) Standard specimen height shall be set as twice the

diameter.

3.2 Sample Preparation

( l) Without finishing lateral suface of the specimen

In case the borehole core diameter is the same as the

diameter of the test specimen, the borehole core shall be

cut to a desired length by a cutting machine. A suface

grinder if required shall finish the specimen ends.

(2) Trimming method

R Test specimen shall be trimmed to a desired diameter,

using sample trimmer, wire saw or straight edge.

R Ends shan be finished using miter box, wire saw, or

straight edge.

(3) Recoring method

R Test specimen shall be recored from block samples

into a desired diameter.

C Ends of test specimen shall be trimmed by a cutting

machine, and finished by a grinder if necessary.

3.3 Specimen Size Measurement

( 1) Specimen diameter shall be measured in the vicinity of

both ends and at mid-height to less than O. Imn, and the

average value of the 3 measurements shall be assigned as

initial diameter Do (cm).

(2) Specimen height shall be measured at more than 3

locations to less than O. Imm, and the average value of the

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3 measurements shau he assigned as initial height Ho

(cm).

(3) Mass of the specimen, mo (g) shall be measured to less

than 0.0lg.

(4) If necessary a representative piece shau bc selected from

the trimmed-off portions, and water content shau be

measured. Measured water content shall bc assigned as

initial water content wo (%).

(5) Initial conditions of the specimen shan be observed and

recorded.

[Notes]

3.1

(2) For coarse-grained or brecciated rocks, or conglomerate, it

is desirable that the specimen diameter be greater than 5

times the largest compositional grain.

3.2

a. It is desirable that the test specimen of weak rocks be made

and tested immediately after samphng. In case there is

duration bctween sampling and testing, care should bc

taken so as not to damage samples, to change water content,

or to cbange sample condition in situ.

b. When preparing test specimens, portions of material, which

are obviously disturbed during sampling, shall be excluded.

c. Specimen shall be prepared within a reasonable duration of

time so as not to change water content of material. Care

shall be taken so as not to disturb material.

d. When preparing specimens, material orientation shall be

recorded for clarity.

e. In principle, material longer than the finished specimen

height shan be usedL

f. Specimen ends shall be fmished ffat to an accuracy of

O.02mm, and square to the specimen axis. The squareness

shau not deviate from its perpendicula:ity by more than

0.001 radians or 0.05mn for 50mm diameter specimen.

g. Lateral side of the specimen shall be smooth and free of

inegularities. It shau be straight over the fuu length of the

specimen. with a deviation less than 0.3mn.

( 1) If material is affected by wetting, it shan be wrapped with

plastic film and trimmed by a cutting machine using a small

amount of water or oil.

(2) If samples are sensitive to wetting, trimming method should

be applied to borehole cores and sample blccks larger than

the specimen diameter.

(3) In case samples are insensitive to wetting, rec(xing method

should be apphed to borehole cores and sample blocks

hrger than the specimen diameter.

3.3

(3) If necessary iuitial wet density, pto (g/cm3), initial dry

density, pdo (g/cm3), initial void ratio, eo, Initial effective

porosity, no (%), and degree of saturation. Sxo (%), may bc

calculated using the following equations:

mo

ptQ - - - -Vo pdo Vo ,

VoPs _1 neo ~ "~ow ~n~s xICO o ,ns ' Inow ~ m*

Sro~ mo~m~ x Ps xIOO ~ Vops ~ m5 p ~

Where Vo (cm3) : initial specimen volume

l Vo = ZiD~HO l

~ 4 ) p* (glcm3) : grain density of rock composition

p~ (g/cm3) : density of water

m, (g) : dry mass of specimen

m (g) : mass after submerging specimen into water

longer t.han 72 hours, and

mw (g): apparent mass in water after submerging specimen

into water longer than 72 hours

(3) When water content is determined on the tested specimen

subsequent to the tcst, water content measurement on a

cut-off piece may be omitted.

(4) Lithology of the trimmed spccimen shall be observed,

together with properties of bedding planes, laninae, and

fissures, and the degrees of weathering and alteration.

Offset angles of the bedding planes, Iaminae, and fissures

from the specimen axis shall also be measured.

4. SPECIMEN SET UP

( 1) Specimen shall bc placed on the pedestal, onto which a

10ading cap is placed. The side of the specimen shall

then be sealed with a covering material. The ends of the

covering material shau bc tightened with O-rings against

the pedestal and the loading cap.

(2) After triaxial pressure chamber is assembled, coifinimug

fiuid shall be introduced into the chamber.

[Notes]

4.a. After placing a loading cap on top of the specrmen

134

excessive seating load shau not be applied in the axial

direction of the specimen, until cell pressure is applied to

the specimen. Especiauy when the compressive strength

of the specimen is expected small, the seating pressure shail

not exceed 10kN/m2.

( 1)a. If the condition specified in Note 3.2f cannot bc met, the

specimen ends shan he capped with materiai likie plaster.

Clapping thickness shall be in the order of I to 3mm. The

capping material should be stronger and more rigid than the

rock specimen.

b. Loading cap and pedestal without drainage holes shau be

used, otherwise flat rigid disks with the same diameter as

that of the specimen are placed beneath the loading cap and

on the pedestal.

c. In case rubber membrane is used, sample set up

procedure may be different, depending upon the membrane

stretcher used.

(i) Wirth two-pieced membrane stretcher

~) Specimen is placed on the pedestal, such that the

specimen is concentric to the pedestal. Capping

material shau be applied, if required.

C Rubber membrane and O-rings are placed on the

two-piece membrane stretcher, and the membrane is

stretched snugly against the iuner suface of the stretcher,

applying vacuum. In this condition the stretcher is put

around the specimen and the pedestaL so that they are

covered with the membrane.

R Capping the top end of the specimen, if necessary, the

loading cap is lowered and touched the specimen. The

loading piston is then fixed to the upper board of the

pressure chamber. In case the loading cap is not rigidly

comected with the piston, it is placed concentrically on

the top end of the specimen to be capped, if required.

~) Upper and lower ends of the rubber membrane are set

free from the stretcher, and the membrane is tightened

with O-rings against the loading cap and the pedestal.

C The membrane stretcher is then split into two pieces

and removed.

(il) With cylindrical stretcher

(~ Test specimen is placed on an appropriate stand.

~ O-rings are put around the loading cap and the pedestaL

This is not necessary when elastic bands are used to seal

the specimen.

R Rubber membrane is placed on the membrane stretcher,

and the membrane is stretched snugly against the inner

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suface of the stretcher, applying vacuum. In this

condition the stretcher is put around the specimen and

the pedestal, so that they are covered with the membrane.

~ Upper and lower ends of the membrane are set free

from the stretcher, and the lateral suface of the specimen

is covered with the membrane. The extra portions of

the membrane are folded back

C Capping the specimen ends if requtred, the test

specimen is placed on the pedestal, such that the

specimen axis is aligned with the pedestal axis. The

membrane is then straightened to cover the pedestal.

C Capping the top end of the specimen, if necessary, the

loading cap is lowered and touched the specimen. The

loading piston is then fixed to the upper plate of the

pressure chamber. In case the loading cap is not rigidiy

connected with the piston, it is placed concentrically on

the top end of the specimen to be capped, if required.

~) The membrane is straightened to cover the loading cap.

R Membrane is tightened against the loading cap and the

pedestal with O-rings.

(iii) In case a membrane stretcher is not used

~ Test specimen is placed on an appropriate stand.

@ O-rings are put around the loading cap and the pedestal.

This is not necessary when elastic bands are used to seal

the specimen.

R The specimen is covered with the rubbcr membrane.

The extra portions of the membrane are folded back

C Capping the specimen ends if required, the test

specimen is placed on the pedestal, such that the

specimen axis is aligned with the pedestal axis. The

membrane is then straightened to cover the pedestal.

C Capping the top end of the specimen, if necessary, the

loading cap is lowered and touched the specimen. The

loading piston is then fixed to the upper plate of the

pressure chamber. In case the loading cap is not rigidly

connected with the pistcu~ it is placed concentrically on

the top end of the specimen to bc capped, if required.

C The membrane is straightened to cover the loading cap.

~) Membrane is tightened against the loading cap and the

pedestal with O-rings.

d. When a heat shrinkage tubing is used, the following

sample set up procedure may be used:

~ Test specimen is placed on the pedestal, onto which a

loading cap is placed. The axes of the loading cap, test

specimen, and the pedestal are then aligned.

~ Heat shrinkage tubing is put around to cover the

loading cap, test specimen, and the pedestal.

R Wrth an appropriate heat source, the tubing is shrunk

till it sticks to the cap, test specimen and the pedestal.

@ Membrane is tightened against the loading cap and the

pedestal with O-rings.

(2)a. Water or oil is generally used as coifining fluid. For

some cases, e.g., at low cell pressures, gas may be used as a

substitute.

b. Triaxial cell shau bc assembled together, folbwing

procedure most appropriate to the structure of the testing

machine used.

5 . METHOD OF TESTINC

5. I Isotropic Stress Application

(1) Load cell and displacement transducer are mounted.

(2) Cell pressure is increased, and the specimen is

pressurized isotropicauy until the cell pressure reaches a

desired initial isotropic stress.

5.2 Axial Compression Stage

(1) Load cell and displacement transducer are adjusted and

initialized.

(2) Keeping the cell pressure constant, the specimen is

continuously compressed in the axial direction, at a

norninal axial strain rate ranging between 0.01 and O. l%

per minute. If it is difiicult to keep the axial strain rate

constant, however, the specimen may be compressed at an

axial stress rate equivalent to the above-mentioned strain

rate.

(3) Axial force, P (kN), and axial displacement, ~ (cm), or

axial strain, e* (~o), are monitored during compression.

(4) For stroke control tests, the specimen sban be

compressed even aiter the maximum load ceu reading is

reached_ Compression may however he terminated in

principle when a residual stress state (no futher principal

stress difference) is reached.

(5) The specimen tested shall bc taken out of the tiaxial cell,

and conditions of deformation and failure shall be

observed and recorded.

[Notesl

5.l

(2)a. When the cap is rigidly connected to the loading piston,

the axial force is applied to the specimen tbrough the

loading piston, simultaneously with cell pressure

application to obtain an isotropic stress state for the

specimen. Since the relationship bctween axial force and

cell pressure may vary, depending upon the diameter and

self-weight of the loading piston, it is necessary to know

their relationship in advance.

b. Circuuferential displacement measurement device may be

mounted if required.

c. Nouinal axial stress rate shau bc iu a range between 3 and

60MN/m2 per minute.

5.2

a. Oven-dried mass of the specimen, ms (g), may bc

measured if required. This procedure may be omittetL

provided the water content has been detemined using a

piece of triinned-off portions of the specilnen prior to the

test.

( l) If required, lateral displacement transducer is calibrated and

initialized.

(3)a. In case the axial conrpression force and axial

displacement are not continuously recordetL an adequate

sampling interval should be adopted, so as to draw a

smooth curve of the principal stress difference vs. axial

strain relationship.

b. Axial strain is monitored by strain gauges mounted on

the lateral surface of the speeimen.

(4) For load control tests, compression shall be terminated

when the axial displacement begins to increase abruptly.

(5) After compression test, the conditions of deformation and

failure shall bc observed and sketched from the direction

where the state of the spechnen can bc seen most clearly.

When a distinct shear plane is formed, the observation is

made from an angle at which the shear plane bccomes

steepest. The shear plane shau be sketched such that its

inclination can be drectly read in the drawing.

Observations are made to evaluate whether the specimen

tested is homogeneous, and what condition impurities are in.

The observation results are then recorded.

6. CALCULArIONS

6.1 State of Specimen prior to Test

hitial cross-sectional area of the spechnen, Ao (cm2), is

calculated from the following equation:

1 el )12

A0= o 4

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6.2 Axial Compression Stage

( 1) Axial strain of the specimel~ 88 (%), is calculated using

the fouowing equation:

ea ~r x 100 ~HO

Where AU (cm) : axial displacement of the specimen.

(2) Principal stress difference, ca ~ (1r (MN/m2), at an axial

strain of ea (%) is calculated, as fouows:

r= ~ j p e a Ao 1 1~ xlO (r

Where

P (kN) : axial compression force exerted to the specimen

at an axial strain of e* (%). P = O in the isotropic

stress state.

cFa (MNlm2) : stress acting in the direction of specimen

axis, and

(;r (MNlm2) : stress acting in the radial direction of the

s pecimen.

(3) The relationship bctween principal stress difference and

axial strain is plotted in a graphical form, where the

vertical axis is the principal stress difference, and the

horizontal axis is the axial strain.

(4) Maximum value of the principal stress difference is

directly read on the figure described in (3) above, and is

assigned as the compressive strength of the material

tested.

[ Note]

6.2 In case circumferential displacement is measured, latenl

strain, e, and Poisson's ratio, v, are calculated using the

following equations:

Al xlOO Aer ' Ir:Do ~ Ae.

Where Al (cm) : circunferennal displacement of the

s pecimen.

(2) Initial height, diameter and wet density of the specimen

(3) Initial water content of the specimen, if measured

(4) Observation results on the specimens

7.3 Items with respect to Test Results

( l) Cell pressure, and strain rate or stress rate

(2) Compressive strength and failure strain of the specimen

(3) Principal stress difference vs. axial strain curve

(4) Observation results of the specimen tested

(5) Relationship between compressive strength and isotropic

stress

(6) Description of test method, if partiauy different

procedures from this standard are adopted.

7.4 Other Special Notes

7. REPORTlNG OF RESUIJTS

The following items shall be reported regarding the test

results:

7. I Items with respect to Rock Samples

( l) Sample location: name of the place and depth

(2) Rock type

(3) Sampling method

7.2 Items with respect to Test Specimen

( I ) Method of sample preparation

[Notesl

7. 1

(2) e.g., sandstone, granite, tuff and so on.

7.2

(2) If requiredj initial dry mass, initial dry density, initial void

ratio, initial effective porosity, and initial degree of

saturation of the specimen shall be reported.

(4) Iithology of the specimen should be reported along with

geological features of the speoimen, such as offset angles of

bedding planes, laminae, and fissures from the longitudinal

axis of the specimen.

7.3

(3) When circumferential displacement is monitored, principal

stress difference vs. lateral stain relationship shau be

reported, if required, together with lateral strain vs. axial

strain relationship and Poisson's ratio.

(5) If necessary, angle of internal friction, c~, and the intercept

at the vertical axis, c~, obtained from the Mohr's failure

envelope shall be reported. If the envelope is nonlinear,

the stress range at which c* and c. are determined shall be

clearly stated.

7.4 a. If required, residual strength of the material tested shall

bc reported along with the angle of internal friction at this

state, c,, and the intercept at the vertical axis, c*, detennined

from the Mohr's circles for the residual stress state.

(2) If requiretL the secant modulus. E*.50, and the tangent

modulus, EL50, for each applied isotropic stress shall be

detennined from the initial portion of the principal stress

difference vs. axial strain curve at 50% of the maximum

strength of the material. The relationship between

deformation moduli and isotropic stress shall then be

- 137 -

reported。

3CO欄三M服ON　T冊ST照正）側》

3．1GENFRAL

3・LI　Tes象PuΦose　a殿d　ApPHca捻on　Range　ofthe　S松皿dard

　To購nde岱㎞d　the　mec㎞cal　be㎞鍍or　of　rock　mass，it　is

veq～㎞portant　to　gmsp　猶πst樋玉e　m㏄㎞cal　beh＆vior　of　the

rockthatconstit鵬sther㏄kmss。Forthisp肛pose，1血説飢

comp【essio蹴tests訂eo負euc面eαout，sincethetes血9

machine紐dmeasuremePtde煽cesrequ血edfor拠eξes㎏㍑

relatively　simpl¢a鳳d　easy奪o臆se。M盆ny　pubHshed幅axial

compressioa　　　test　　π｝s“1総　　　a∫¢　　　ava溢b1¢，　　i鳳clud血g

cross－reぬtionshipswitht藪e爬su猛sofo山err㏄ktests。Itis

however　d棚c皿t　to　describe曇獄Hy　the　rock　behaviors　wi象h重he

uniaxial　compBssion象est　resu玉ts　ody，when　st爬ss　con（韮tions

aro　comp韮cated　as　in　the　vich盛ties　of　huge　b【idge　found戯樋ons，

dam　fomda“ons，or　undef餌omd　st瓢ctufes．The　stてength㎝d

dβ£or㎜tio礁　charac胎纐stics　of　t魅e　rock　obtai聡ed　角rom　the

面a】dahests　become　esp㏄ially　impo出mt　for　the　desi餌of

t盤eses㎞ct町es。lnevalm血gt紅es登en幽＆ndd。f・㎜亘6n

c㎞ctedsticsofther㏄kwit蝕td蘭alcompressio凱陀sts，itis

臓ecessaぽy　to訟ke　t盤e　d血ge　co獄dition　du血g　the驚sts血to

considera振on，　with　respect　to　the　designed　s1騰cture　a駐d

lo盆ding　typβs，and　t血e　t血e　pe謡ods　of　tbe　co盤碗c亘o疏．　For

example，when　a　long－tem　s訟bi磁y　problem　is　considered，t血e

tests　sho皿d　be　co“ducted血co繍so狂da槍d　drah｝ed　condidoo　and

tむe㎝eepProわlemshou互da㎏o塊accomtedfof．V磁磁tyof

apPlyiBg　the　eff㏄dve　stress　co皿cept象o㎞ぼd　r㏄ks　sho題ld　be

examine¢depen｛盤nguponthest曲1㈱s翻sedinthetes蕊，

s血ce　hard　r㏄ks　genefany　have　high　s従ength　a簸d　ve可10w

porosity・The凪f併eitisno£commo臓tomeasurep倣ewater

press騒re㎞triaxial　compfession胎s捻㎜d血axial　compression

stages　i皿p俄ct量ce。　Unde罫the　assumption　that　tぬe　pofe　watef

pressufe　has　H就le圃“ε鳳ce　o逓the　mec㎞cal憂》e血avior　of　the

f㏄k，セiaxial　tβsts　am　臓suaUy　cond腿c惚d　on　natuπany　面ed

samples祓赴oatd面皿ge．Fofthisleaso鶏thes紬d寵

descdbedhefe配丘nesb舗altests？e㎡o㎝ed轍hthedra㎞gev盛vecloseαas㎜dr滋neda加unconso狂dated（U切

conditio凪F賦ね㎝nore，exampletestresultsshownare詠ot

e魅th鷺1y　for　satum』ed　sa江【茎》les．　The　s綴ndard　ain器画hly　for

satu鷲」ted　samples，yet　may　be　app｝icable　to　partiany　satura1£d

samples，toO働

　1繊th三s　s㏄tio臓，so負r㏄ks　are　d量s之ingu狛hed　fピom　h紅d　r㏄ks，

accαding　to　the　uniaxial　compressive　strength　gu：Soft　rocks

㎞veg．lesst㎞10t・20MN／m2，while㎞dr㏄㎏㎏veg。

more㎞50to100MN／m2．NotethatthosevaluesarevaM

for　　isotropic　　㎜teria始．　　　Aniso虻opic　　㎜te雌曲　　with

撫血tio魏s　a臓d短ye爬d　s象r㏄mres　w簸1be　discussed㎏ter．　For

so負r㏄ks　to　wh三ch出e　concept　ofef箔ecdve　stτess　is　appHcable

based　o臓Tlerz＆ghi’s　the（｝尊，t血e　h真ter脳級重dc憶o鳳al孤gle　of　the

㎜tedal　exP⑱ssed　in　ter螂of　to観st鶴ss　can　be　zeぎo　under㎝

condi昼on．　　　Figuτe　　Ll　s血ows　山e　results　of　蜘樋

compressio麺（UU）tests　o丑S麺咽㎞mudsto獄e．Tho“gh　there

is　some　sca耗er，increase血sセength　ca職not　be　seen　ovef　a　ceU

press町e㎜gebetweenO孤d2MN／m2。Thism㎝蹴hatthe

sampleisf憾ysaturated，andthatthein㏄easeincenpress鵬

拾compensatedbytLe血cre＆sei脚o艶pressure，keepi無gt蝕e

ef玄eCtiVeStfeSSCOnStant．

　0蹴t簸e　ot蝕er　ha獄d，Figufe　1．2s蝕ows　the　results　obta㎞ed

盤om　the　t【iaxial　compression　tests　o戯a　h紅d　rock　The　figure

i腱dicates　t］皿t　the　s捻engtむis　obviou購1y　depeadent　on　the　ce狂

pressure。As　w澄1be　disc腿ssed　in　Sec昼on3。L3，it　is㎞o職

th＆t　there　is　a　range　of　sむ℃ss　whefe　ef∬㏄丘ve　stress　pri纏ciple

apPHes　dependiug　upon　the　s錠a血mte，oven廊or　bar｛1foc1【s　with

porositieslesst㎞1％．Thisimp猛esthatthe閃“atio腱to

descdbe　e飾㏄娠ve　s鞍ess　co㏄spo紅ds　to聡種臓tion　1血Sectio麺

3．1．3，where　t瓶e　com診ress三bi旺ty　of　wa鈴r　an（l　so弧skeleto臓is

睡n血to　co且sidera“on．　Fuτthe㎜o鷹｝，a　rapid　advance　血

　1．5

貫＼1．0之窯

）O．5k

0

φ騙需0。

ら篇玉．15MN〆m2

　O　　　　　　l．0　　　　　　2，0　　　　　　3．0　　　　　4．0

　　　　　　　　σユ，σ3（MN／m2》

E騨e1．1M・㎏’sckdes歓UU鰍s（S効・41））

9》浮5

9さ

～

　　　護　　就

諺

　　　　　　　5　　　　　　　10　　　　　　σ（×103M賛〆m2）

Fl騨e1．2　　Fa弧uτe　e【夏ve夏op　ofrock㊤臓c♂））

一138一

numerical analyses in recent years has made it possible to

describc in detail the characteristics of rock mass with different

models, including one that considers the effect of

discontinuities. In conducting these numerical analyses, it is

very important to understand the mechanical behavior of the

rock itself.

From the above viewpoint, experimental researches for rocks

will be reviewed frrst. The mechanical behavior of the rocl~

different from soil, wnl then bc discussed in detail.

3.1.2 Advancement in the Research into Mechanical Behavior

of Rock

From the mid 1960's to the early 1980's, to understand the

earthquake mechanism and the iuner structure of the Farth,

many researches on hard rocks had been conducted into the

effects of temperature, isotropic stress (intermediate stress),

strain rate, sample size and anisotropy. Published papers dealt

with wide variety of subjects, such as failure criteria, the

development of the hacture within the sample, and the change

in elastic wave velocities. These papers bave been reviewed

carefully in the book called "Experimental Rock Mechanics"

by Paterson35). According to the book the frst paper was

E:

,~ ~ ~'k,: :~¥~:~'

~;~ x:~4 q'v~)

F:~~3 q;*x

:1::: q,9 ~ h;:~ ~u' e'c" ~:: e, c"hl ~~~:L c~-'~S ~S O ~S U ,~

published by Karman22) also very famous for Karman's eddy

and the column's buckhng theory. He presented the

experimental results on Carrara marble performed under an

accurate cell pressure control. Wirth uniaxial compression

strength of 140MN/m2 in a high-pressure triaxial cell with a

maximum ceu pressure of 326MN/m2, he showed that the

strength is dependent on the mean stress and that the marble

possesses both brittle and ductile failure characteristics. The

crystal structure of the marble after failure was also discussed,

based on the consideration of the friction law, and the

observation results under microscope.

Failure phenomenon of buttle material like rocks attracted

many researchers, Griftiith~4) to begin with, whose interest were

mainly theoretical developments. Here focus is placed on the

experimental work where micrccrack developments were

observed in some mauners. Generally speaking, in the rlfst

stage of a triaxial compression test on brittle material like rocks,

pores begin to close due to the increase in principal stress

difflerence, and the stress-strain relationships become convex

downward. In the second stage, elastic behavior prevails, and

the stress-strain relationship becomes fairly linear, though

hysteresis stm exists. In the thrd stage, a steady crack

Steps in areal density of microcracks

g 6-8;6:o

~} 4-6;~o

~l 2-4;~:o

~ O-2;~D

~] O;~;s

[1] Fractured during preparation of thin section

C / ll / /

l* /

A

B

/ / / ll / / / Cell pressure _//

/ / /

D Principal stress difference

Fignre 1.3

o.S (r 0,g5 cr c:~cat cr~** 0.98 (1~.. ~** ~**

Region AB Region BC Region CD

Stress-strajn relationship and areal density of microcracks in quartzite (Hallbauer et al.15))

- 139 -

development may be observed and the axial stain stays linear

but the lateral strain becomes nonlinear. As a result, the

volumetric strain becomes nonlinear. In the foUrth stage,

fractures occur in particle structures within the zones of

developing unstable cracks. Detailed descriptions are

swnmarized by Paterson3e)

It is therefore natural to expect these changes in rock

structure be observed directly in experiments. rlallbauer et

al.15) carried out a serics of triaxial compression tests on a

fine-graiued quartzite. They loaded the specimens to different

stress levels, and took the specimens out of the triaxial cell.

They then measured the difference in areal density of the

microcracks in vertical section at each stress level prior and

subsequent to fajlure. Not to mention, a loading frame with

high stiffness and technology to measure the microstructure of

a rock were required. In the experiments, they observed over

2,000 microcracks in a 75mm long, 25mm diameter specimen

of a quartzite, and calculated the crack density for a unit area of

4mm2, as shown in Figure I .3. It is reported that the length of

the cracks observed was between O. I to 1.0mm, and that most

microcracks occurred within the quartz particles. Detailed

investigation revealed that the mean length and the mean width

of the cracks were 3COum and 3mm, respectively. Most

microcracks were oriented at angles less than 10 degrees to the

longitudinal axis of the specimen.

It may also be seen in the figure that a localized deformation

occurs even at low stress levels, and that zones of connected

discontinuities are formed in the central portion of the

specimen right before the peak strength is reached. This

phenomenon is universal though it may be dependent on the

mean stress. These are stress-induced cracks and are different

from liquid-solid interfaces often found in quartz particles, and

~ 800 ~ Z ~:

e' 600 v r: (u*

'u

~ 400 ~ o ~:;

u'

~~

~ 200 u ~:

~u

o

Cell pressure = 100 MN/m2

Ct - -- -r---- ---"- -I

/

/

/

/

Ev al r ~ es C, ,11-,'1~

o , 004

L-J

l 500

~ ¥ ~ ~:

q,

u ,:: 1000 e,

s,

~: ~ s,

~ ~ 500 I~i

~ "v ~

'i::

f~

( a) Strain

Cell pressure= 400 MN/m2

C;d

n

Oo 0.5 1.5 l.O

Axial Strain (~6)

~;

¥ 15 -

~ 10 '5S

~ ~Q

~ 5 V,~'F:

:sc'

~~

(c)

'* I'L";ti ' " :":ne"rJ:/

:~~~~;f~!:":'~i'- 't .~' ¥' .. t 'r'~e:"~ ' ~ '

r'~:L?~~'~' *.. :t

: "'

.. .¥1(!~/:::~ .1

,;:#. ':.'t;: ":

~f~~~T~~~:~..i--t: ' ?"I :;t _.. ,1

..1-* . * ,* .. .. . ' * '1 ' '_ "f'* j "-" '

I

( b)

H HI iv v VI

o

Figure I .4 (a) Stress-strain relationship of Westerly Granite at cell pressure of 100MN/rf (Braee et al.5))

(b) AE signais associated with failure of rock (Schoiz39)), (c) Generatton process of ~aultmg estmated ftom AE observation (Lockner et al 31))

- 140 -

consisting of microc.racks with a diameter of about 10mm.

These liquid-particle interfaces are inherent cracks. Kudo et

al.30) observedthese cracks in various Japanese granites. They

investigated in detail the relationships with mechanical

anisotropy caused by the fabrics and structures of granite.

Peng & Johnson37) and Olsson and Peng34) studied the

geometrical characteristics of crack formations in different

rocks, though the basic idea was the same as ffallbauer et al.Is)

Lockuer et al.31) observed the crack development using acoustic

emission technique. In their experiments, to prevent cracks

from developing too quickiy, axial load was carefuuy applied

with a hydraulic servo control system, to produce the test

results shown in Figure 1.4. Vmegar et al.48) observed the

inside of a specimen with a computer tomography (CT)

technique. It was found in their research that even though the

density change of a rock is regarded isotropic under hydrostatic

pressure, dilatancy (volume increase) due to the development

of microcracks might occur in the central part of the specimen,

while density increases (volume decreases) at the ends of the

specimen under uniaxial pressure. The CT machine has an

accuracy of detecting the O. I % change in 2mm2 of CT figures.

Wang et al.49) developed a laser speckle method to observe a

fracture process zone occurdng at the tip of a fracture. This is

an effective method in observhrg the development of failure

area in a spocimen continuously without physically touching as

load increases. Furthermore. Sugawara et al.43) continuo th~ir

observations of different geomaterials from soft clay to hard

rock with X-ray CT machine.

3.1.3 Concept of Effective Stress for Rocks - Verification by

Experiments and Effective Stress Representation

Biot3) flfst proposed a concept of effective stress and

established the theory for rocks as a porous medium. His

research was introduced by Jaeger & Cookzo) and Paterson35)

Skempton42) evaluated the compressibility of soil skeleton and

soil particles, in which he assumed the Terzaghi's effective

stress concept is valid for soils. Brace & Martin5) studied the

validity of effective stress concept for Westerly Granite with a

porosity less than I %. In the experiment, the principal stress

difference under triaxial compression was measurled with strain

rate ranging 10:7 to 10'3 (s~1), as shown in Figure l.5. In

Figure 1.5(a), white circles and white triangles respectively

represent the resuits for dried and wet specimens at a cell

pressure of 156MN/m2. Black circles and black rectangles

represent the results for wet specimen with an effective ceu

pressure of 156MN/m2 by apparently contromng pore water

pressure. To investigate the chemical efriect of the media used

for applying ceu pressure, two kinds of liquid, water and

acetone, were used.

Figure I .5(b) gives a conceptual description of Figure I .5(a).

It may be seen in the figure that the strength of the specimen

graduauy increases with the increase in strain rate in area BC,

suggesting the strain rate dependent nature of the material.

The results for dried or wet conditiolL or even for CU condition

follow the same linear trend. It is, therefore, reasonable to say

that as long as the strain rate does not exceed the point C, the

concept of effective stress is valid even for the rock with

porosity less than 1 9~o. Brace & Martin5) caued the strain rate

at point C a critical strain rate. For a strain rate above point C,

even if the pore water pressure is controlled, the pore water

pressure camot dissipate fuuy within the specimen, as the

strain rate increases, as shown by the black circles and

rectangles in Figure 1.5(a). In this case, the strength given by

the principal stress difference inereases. They called this

phenomenon as 'dilatancy hardening' . It may be understood

from the above discussion, that there is a certain range within

8 ¥~ 1 600

~:

e'

v f::hsJ 1 400

~ 1:'

e' +**~ I zoO

fs'

,:~

u F;

~ I OOO

･ Water I f CeH pressure 312MN/m2

･ Acetone f k Pore pressure 156 MN/m2 a Water I f Ce]1 pressure 156 MN/m2 Q Acetone J I Saturated with pore ~uid

* Dry

S a

~~ E~

R~~

A A

A ~ O l~

f E

Pore presstlre // D

¥ / f / /

// Dilative Critical st~ain rate,// hardening

!

/ / / B C Dry or saturate(:! with pore fluid

l0-7 -6 ro~s ro-3 Straln rate --~ ro-4 ro

(a) Strain rate (s~1) (b) Figure I .5 (a) Influence of strain rate on failure strength of Westerly Granite at effective confinhrg pressure of 156MN/rf

(b) Schematic diagram ofdilative hardening (Brace & Martin5))

141

whichtheconceptofe舳ctivestless瞭hs画nmtedependency　is　vaHd∬or　rocks　wit勉po1osi砲玉ess　than1％。

Acc・血gt・Badi鋤ski＆0℃・㎜eHη，there膿t㎞e

possible　states　of　the　water　exist血g血po翼es1三ke　cracks＝1）

f皿y　drai蹴e（1；　2）　md面獄ed　co㎜ec憾o臓；　and　3）　undra血e｛i

iSOぬtiO紬．FOreaC血S蝋e，aSelf－CO鶴SiSte飢SOIUtiOneXiStS．

ThesolutioΩsuggeststhatelasdcmdulusofa皿te由私

㎜croscopica冠y　e（luivalent　to　the　㎜胎豆a蓋　with　cracks，　is

k紅gelydependento惣thede鎚ityofthecmck　Forexample，

the1mcroscopic　Poisson’s　ratio　d㏄reases　wi象h血e　iacrease血

cfackde那ityunderd曲edcondition，andincleasesundefun血inedc・nditi・鎚．Bi・象3）pr・P・sedthe嫡・wiagequati・・

餓㎞g　water　pressurc　within　a　crack血to　acco㎜t：

σ麟一2σ⊂ε群1義vε肱δ輸）（1）

Where，σ畦is＆s鵬sstensor，αisacoe衝cient，〃幅erpressure，

鋤dδ醸Kro麺ecker’sdelta・　σaadv鉱eresp㏄dvely

macroscopic　s蝕ear　modulus　and　macmscopic　Poisson’s　mtio

εof　mato憾als　with　cracks．　It　was（雌行th互4》who　stu（澄od

logicaUy　the丘acture　theo鯉for　r㏄ks　with　this　c㎞ac塾edstics。

J縦eger＆Cook30》expamded甑e　t蝕eo耀to　the　case　where　water

pressure　exists．　Denoting　te獄s簸e　strength　by　Zo，they

expresseαfail縫re　c謡teda，as　fonows：

　1）forσ1÷3σ3≧4ρ

　　　（σ、一σ3）2－8瓢。（σ、＋σ3－2ρ）諾0　（2）

　2〉f㎝σ1＋3σ3＜4〃

　　　σ3嵩一2b＋ρ　　　　　　　（3）Though　these　e〔lua戯ons　do　not　翻ecessar簸y　s哉廊取　aH　the

s鵬ngt紅co聡di乞ions，藪a盤ure　c亘胎ria皿y　be　expressed　wit血o騒t

血clu（簸鶏g　water　p爬ssロ鴉，ρ，　wheB　an　e鎚ective　stress

represe聡伽on，σ’軽濡σザαPδ嚇，isapPHedtot無eequa丘o鵬・

It　iS　Very　血PO漁簸t㎞　血胎Ψre血g　tむe　eX茎｝e盛men監a玉feS戯tS・

Note　that　a　paぼabo韮c£a逓u爬｛酒£eτion　sho鴨血Figule　12狛

aおo　apPHcable　to　the　co職di“on蓋）。

hsumma＝y，血e鋤uτes重rengthofr㏄ksmaywe簸begiven

血　ter螂　of　effective　s“℃ss　eveB　岱or　hard　rocks，　whe血　the

load盤1g　fate隻s　very　slow　or　the　t㎞e　for　pore　water　press臓e　to

dissip田£is　long　e110ugh．　Note　th説exp鵜ssio鵬蚕orαhave

わeen　studiod　by㎜y　researchers。

3．1．4A鶏isotropy

D・mthg）stu戯ed罐s・紋・picbo㎞vi・mfr・cks．FigweL6

gives　an　example　of　his　test　results。　V而en　the　r㏄k　mass始

obviously　an至so継℃pic，there　are　cases　the　sセength　aniso鉱ogy

s赴ould　be　exan重臓ed　re㎞tive　to　the　principal　loading　dkection．

3。2卜rEST　APP㎜S

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70MN／m235MN／m2

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Fig瓜e蓋．6　　R£㎏tionsh垣s　ofc！eavago　angle　and　p血c嘘》a蓋s賞e6s

鹸renceat憾ure血t曲dalcompress量omestson鋪atedrocks。　　　　Thece皿pres瓢es騰sbow駐血癒e盛9臓ros．　（a）Phylhte（Donath9》），（図）S㎏te（McLamore＆Gray32））

3、2．1Conventio面丁㎞al　Compfession瓢est　Machk監e

3．2．1．1　　】〉㎞dmum　　（》】匿　　Pressure　　a獄d　　Maxilnum　　緬a直

　　Compressive　Force　（Study　Co側11ee　for　U勤iaxial　a血d

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　Tho　n㎞mum　cen　pressure　vades　depending　upop　whether

由e　rock　is　so丘or㎞rd．　For　so丘rocks　it　is　co㎜only　less

重㎞10MN／m2，wMeitis・臨n㎞gert㎞10MN／m2f・r圃d

r㏄ks．　顎e　medium　used50r　apPlyi鳳g　ce皿pressure蛤usuany

wat¢r　for　so負rocks，and　o慧fαr　hard　r㏄ks．　】［臓ge鶏㎝110ad血9

c＆paci砲of　the　apPala鵬is㎞the　o奮der　of20to500kN　for　so負

r㏄ks　and200to5，000kN£or　hard　rocks．　Load㎞g　method　is

曲o（雌ere鳳t：　Mos亀so負f㏄k　apPa曜駄tus　use　a　stadonaτy　upPer

Ioading　mm　with　a　motor－or　hyd臓面cany－driven　lowef

loading　ram．　The　upPer　loa（温毅9！㎜is撤ed　as　foτsoft　rocks，

bロt　the　loweτ10ad血9㎜is　drive臓hyd臓u鼓ca旦y盤｝most㎞d

rock　apparatus。

　The　r…gidity　of　the　loading　fヤame　shoukl　be　comside【ed

according　to　t無e　s鉱eng£h　a臓d　the　sti」㎞ess　of　the　rocks硫sted・

Fo∫most　so丘rocks，a㎞e▽威th　modcrate　st置血ess　is　used．

For㎞d　mcks，however，丘ame　stiffness　should　be　high　for

co∬・ect　loa（I　co鶏trol　throughout　the　ent註e　loading　Pてocess，a∬d

for　an　accurate　monito血g　of　posトβeak　behaviors・　　】【t　is

一142一

desirable to use a loading hame with high stiffness in order to

measure the stress-strain relationship accurately in the vicinity

of the maximum load, and in the post-peak stress state. For

example, stiffness of at least 2MN/cm is required for soft rocks,

and 10MN/cm for hard rocks.

3.2. I .2 Precision of Cell Pressure Control and Measurement

Precision of cell pressure control is expressed differently,

depending upon whether or not the cell pressure is larger tban

200kN/m2. For pressures less than 200kN/mz, the prccision is

evaluated with an absolute pressure value; while it is evaluated

with a relative value to the cell pressure when pressure is hrger

than 200kN/m2~ Precision is evaluated with the absolute valuc

in the small pressure range so that the precision is always better

than ~t 4kN/m2. When the cell pressure is supplied by ak

pressure, the pressure control valve that satisfies the above

mentioned capacity and precision should be adopted. When

the ceu pressure is supplied by load through a piston cylinder

(e.g., NGI type), it is necessary to verify if the precision

specified here is satisfied by calibrating the relationship

between the supplied pressure and the load.

Precision of pressure measurement is the same as that of the

ceu pressure control: For pressures less than 200kl(/m2, the

precision is evaluated with an absolute pressure; whereas it is

evaluated with a relative value to loading pressure when

pressure is larger than 200kN/m2. Precision is given in the

absolute value in the small pressure range so that the precision

is always better than !!: 2kN/m2

3.2.1.3 Load Cell

Estimating the compressive strength of the specimen,

maximum axial compression load subjected to the load cell is

calculated using the specimen diameter. Among several load

cells with different capacities being preparedj a load cell to be

selected shau have loading capacity larger than the estimated

maximum axial compression load and required measurement

accuracy! Tolerance of load cell to the maximum compressive

force is specified as big as that for the ceu pressure.

The load cell can be installed within or outside the pressure

chamber. For those used inside the chambcr, the load cell

value can be directly read. However, when the cell pressure is

very large, it is necessary to venfy if the load cell value is

stable and not drifting. In additio!~ some load cells on the

market are self-calibrating types, and they are structured in

such a way that the effect of the change in cell pressure on the

reading can be automatically cancelled out.

In case a load cell is used outside the pressure chambcr,

measurement error will increase when a sman stress is

measured or the piston is subjected to a bending moment. It is

necessary to make some corrections for the frictional force

between piston and bushing of the pressure chamber.

Mounting a load cell outside and another inside the pressure

chamber, and applying an axial force on the loading piston with

a desired ceu pressure, this frictional force can be evaluated as

the difilerence in readings between the two load cells.

Load cells mounted inside the pressure chamber are

becoming popular in recent years, especiauy when measuring

extremely small strains. Generauy, the accuracy of load

measurement is not so good as that of deformation

measurement. Therefore the future challenge will be how to

improve accuracy of extremely sman stress measurements.

3.2. 1.4 Defonnation Transducer

For axial displacement (axial strain) measurements,

displacement transducers are set in place, in such a way that a

relative movement between the specimen bottom and the

loading piston can be monitored. Differential transformer

type displacement transducers, non-contact type proximeters,

electronic dial gauges, and magnet-scales are generauy used.

In case main objectives of the test are to know defonnation

characteristics of the specimen at very small strain levels ,

and/or with high precision, axial displacement (axial strain) is

directly measured on the side of the specimen, using strain

gauges or LDT (Local Deformation transducers). Figure 2.1

r:=::

Inner load cel~

LDT LDT

Figure 2,l

Extemai displacement gauge

Upper platen of triaxial cell

Cap Porous stone Nylon mesh

Filter

paper Steel p!aten

l

Gypsum

Rubber membrane

LDT

Attaehrnent

C.ypsum Ghle Axial strajn measurement using LDT (Goto et al,12))

- 143 -

shows an example of the axial displacement (axial strain)

measurement with LDT (Goto et al.ra)).

Circumferential displacement (circunifierential strain), or

latenl displacement (lateral strain) is usually measured using

strain gauges, ring type transducers, circunferential transducers

and so on.

3.2. 1.5 Cap or Impervious C.ircuhr Disc

When a testing apparatus uses a loading cap and a pedestal

with a drainage hole or a porous disc, an impervious circular

disc whose diameter is the same as the specimen diameter is

usually used. In case a smau deformation of a rock is

measured, the stiJ~:ness of the cap or pedestal should bc higher

than the rock stiffness. This is why special steel for

high-s peed Inachining tools (SKH), and

nickel-chrome-molybdenum steel, (SNCM) or the like is used

as material of the loading cap and the pedestal in testing

crystalline rocks such as granite. SKH is heat treated at

1 ,300 ~C, and can be used in tests at temperatures up to several

hun(lreds centigrade. It consists of chrome, molybdenun~

tungsten, vanadiun~ cobalt and so on. For test at ambient

room temperature, SNCM is used. There are other materials

used, such as nickel-chrome (SNC), and chrome-molybdenum

steels (SCM).

3.2.2 Other Accessories

3.2.2. I Rubber Membrane or Heat Shrinkage Tubc

Rubber membrane should be about 40mm longer than the

specimen. Its thickness should be carefully chosen to avoid

rupture and air/water leakage. It is usually 0.5mm thickL In

ou tests, undisturbcd specimens are used, and soil particles or

shells larger than sand particles may rupture the membrane.

Much attention should therefore be paid to its thickness.

Rubber membrane is usually made of natural rubber, silicon

rubbcr, neoprene rubber and so on. Since heat shriukage tuhe,

usually made of fluorine resin, is hard, it is only suitable for

specimens with small deformation, such as hard rocks.

Usual setup method of the rubber membrane is to put a thin

tubular membrane around a specimen. Occasionally liquid

silicon rubber is directly painted onto a specitnen with a brush

and the test. is performed after the painted rubber dries up. In

special cases, such as long-term tests, tests with high

temperatule and high pressure, care must be taken for the

possibilities of deterioration in rubber membrane (e.g.,

Koizumi et. al.27)) and medium liquid seepage into specimen by

osmosis (e.g., Takahashi et al.44)).

3.2.2.2 Membrane Stretcher

The membrane stretcher is usually selected according to how

the loading cap is counected to the loading piston. When the

cap is rigidly fixed to the piston, a two-piece stretcher is use(L

Otherwise both two-picce and hollow cylinder stretchers may

bc used. In either case, the stretcher should be manufactured

smoothly so as not to scar the rubber membrane. The

diameter and height of the stretcher should be approximately

5mm larger, and about 10mm higher than the specimen

dimensions .

3.2.2.3 O-Ring or Elastic Band

In case O-rings are used to fasten rubber membrane,

espcciauy when a thick membrane is fastened, the membrane

should be wrinkle free and free of sand particles so as not to

cause water leakage. Metal hose clips or metal wire may also

be used in place of O-rings, In such cases, there is possibility

of water leakage at knotted parts on the outer circuniflerence of

the membrane, when the cell pressure is high and the

membrane is thick To avoid leakage, it is recommended to

use more than one clip or more than one loop of wire.

3.3 SPEaMEN PREPAI~IION AND MEASUREMENT 3.3.1 Specimen Size and Shape

Fundamental shape of the specimen used in a conventional

triaxial compression test is in general cylindrical. This is

common to all suggested test methods and standards, regardless

of which institution may be (e.g., ISRM18) or ASTM). The

standard height and diameter of a specimen are respectively

l0.0 and 5.0cm. Depending upon the purposes of tests and

the status of the specimen, the diameter may vary in a range

between 3.5 and 50.0cm and the height between 8.0 and

IOO.Ocm.

For soft- and hard-gravely rocks, conglomerate, relative

gnvel size to the specimen size may become a problem.

When the gravel size is much smaller than the specimen size, it

has no effect on the strength. The ratio of the specimen

diameter (D) to the gravel (d~~ varies in general from 5 to 20.

It is reported by Kawasaki et al.23) that when this ratio is

bctween I and 10, there is no size effect on the uniaxial

compressive strength. In the ISRM standardlg) the ratio is

specified to be hrger than 10. In the Japanese Geotechnical

Society standard (JGS 0530-2000: Preparation of specimens of

- 144 -

unchanged during the sample preparation.

~ ¥ ~; 270 ~:

, ~) 260 ~; 'l'

u'

cu

~ 250 ~ e'

* c~ ~ o Z40 u ~:: qJ ~~

~ Z30 u F:

;~

l 2 3

Ratio of height to diameter

4

Figure 3.1 Shape effect on unconfined colnpressive strength of Westerly Granite (Mogi33))

coarse granular material for triaxial tests), the ratio D/d~* > 5

is permitted. In this standard, it is therefore stated desirable to

use a specimen with the ratio of D/d~* hrger than 5.

For cylindrical specimens used in conventional triaxial

compression tests, it is knowa that there is shape effect as

shown in Figure 3.1 (Mori33)). This is due to a confi'ming

effect from the frictional force between loading plate and

specimen end. To reduce this effect, the ratio of height to

diameter should have a value larger than 2.0 to 2.5. This

value is usuauy set at 2.0 (Study Committee for Uniaxial and

Triaxial compression Test Method for Rocksl9)). In the ISRM

standardl8), the ratio is assigned to bc 2.0 to 3.0.

3.3.2 Preparation of Specimen

Trimming is a method of preparing soft rock specimens. In

preparation with kuife, attention should be paid not to disturb

the specimens. Applying bending moment should be avoided.

If the change in water content is expected to affect the

specimen condition, it should be trimmed as quickly as possible.

In addition, sample disturbance at the ends and side suface of

the specimen should be minimized. In recent years, machines

to finish specimen sides are developed for frozen samples and

soft rock samples. With these, sample preparation time can bc

shortened, and human error due the difference in workers skins

can be reduced (e.g., Koizumi et al.28)).

In hard roc~ there are two methods of preparing specimens:

one is re-coring specimens from block samples in the

laboratory; and the other is to use directly drilled cores. The

latter is very popular. The end sufaces of hard rock

specimens are usually ground with suface grinder.

For both sofi and hard rocks, it is very important to keep the

physical properties (e,g., water content) and the mechanical

properties (e,g., compressive strength) of rock specimens

3.3.3 Specimen Measurement

As for the initial condition of the specimen, recording

discontinuities in the specimen can be helpful to understand

and interpret the test results. Therefore it is important to

observe and record inclination angles of bedding planes,

laminae, and cracks from the specimen axis, and geological

infonnation related to rock characteristics, such as grain size.

3.4 SPEaMEN SETUP 3.4. I Notes on the Use of Heat Shrinkage Tube

Heat shrinkage tube is used mainly for hard rocks, since it is

stiff and its effect on the specimen deformation can be

significant. Heat shrinkage tube is specially processed such

that it shrinks back to the original size upon heating. It is

made of fluorine resin, silicon rubber and so on. When heated,

the inner diameter of the tube shrinks to a size a little smaller

than the specimen diameter, and the tubc sticks to and wraps

around the entire specimen. Heat shrinkage tube is usually

fixed to the loading cap and pedestal of the loading frame with

O-rings .

It is reported in a research paper by Osada ct al.35) on the

confining effect of the heat shrinkage tube, that a cell pressure

becomes about 50kN/m2 in the initial stage when a tubc is

applied, and that it increases to about 200~N/m2 in the failure

stage by axial compression. When the specimen side is

uneven, additional care must be taken, since shrinkage tube

may tear at the comer of a concavity.

3.4.2 Notes on Direct Application of Silicon Rubber

When coating a rock specimen directly with silicon rubber, it

is difficult to apply a thin layer, and the layer tends to become

thick Silicon rubber is therefore used mainly for hard rocks,

such that the effect of silicon rubber on specimen deformation

can be negligible if the layer is thick and stiff.

Silicon rubbcr is divided into two groups: one-component

type and two-component type. One-component type reacts

with moisture in the air and solidifies, when pushed out of a

sealed container such as tube and cartridge. On the other hand,

two-component type consists of a rubber base and a curiug

catalyst. When the catalyst is added and mixed with the

rubbcr base at a normal temperature, it solidifies and bccomes

an elastic body. An attention should be paid, since snicon

rubbcr sometimes attacks copper.

- 145 -

3.4_3 Cell Pressure Medium

Air, water or oil is used as cen pressure medium. An

advantage, when air is used, is that waterproof measure is

umecessary for measurement devices, such as strain gauges.

Acrylic pressure ceus are safe because tensile loads are

designed not to exceed one-tenth of the tensile strength. It is

however very dangerous and the pressure cell may explode at

high pressures if it is defective. It is therefore desirable to use

air pressure not exceeding IMN/m2.

When water is used as cell pressure medium, it should be

deaired in advance. In addition, prevention measures against

corrosion on metal parts, and waterproof treatments for st:ain

gauges are necessary.

Mineral oil is usually used as cell pressure medium. The

advantage to use mineral oil is that strain gauges can be used

'as are' because the oil is electrically non-polar. on is divided

into two groups: pressure bearing oil and heat bearing oil; the

latter is used for tests at high temperatures.

Attention should be paid to heat bearing oil like silicon oil,

since it pemeates through rubber membrane and/or heat

shrinkage tube of silicon rubbcr. In cyclic loading tests, a

measure should be taken to cool down the pressure medium oiL

because heat is generated due to oil viscosity.

3.5 Tl3STING METHOD

3.5. I Application of Cell Pressure

When the specimen is set up in the triaxial celL the

10ngitudinal axis of the specimen should be concentric to the

central axes of the pedestal and the load cell. After the

specimen is placed, the cell pressure medium is introduced into

the cell. When water or oil is used as cell pressure mediu!~~

air is first purged from the triaxial cell, and the cell is fined

completely with water or oil. The loading platens are then

carefuily placed against the specimen, and the cell pressure is

increased to a predetermined level using hydrauhc pump or

other pressurizing devices. The cell pressure should bc

increased at a constant rate as much as possible, and the

defonnation of the specimen during application of cell pressure

should be continuously monitored. Once the cap is firmly

fixed against the piston, the axial load and the cell pressure is

increased simultaneously until the predetermined level of the

cell pressure is reached. Since the applied axial load is

dependent on the diameter and weight of the piston, it is

necessary to determine beforehand the axial load required to

reach the selected cell pressure. After the hydrostatic pressure

reaches the predetermined value, the axial load is increased

while keeping the cell pressure constant until the corresponding

peak strength is observed in the axial stress-axial strain curve.

Furthermore, in case the output of displacement transducers is

not initially steady because of the temperature or cell pressure

fluctuation, the axial load should not be increased until after the

outputs become steady.

The cell pressure should be measured with pressure-indicating devices (pressure gauges or pressure

transducers) during the test. The cell pressure level is chosen

taking into consideration the design and construction depths of

the ground for which the test results will be used. The

capacity of the triaxial cell must also be sutficient for the test.

For example, a maximum capacity of several hundreds of

MN/m2 may be necessary for hard rocks, while several MN/m2

may be enough when testing soft rocks. Since the maximum

depth that man can reach directly at this moment is about 3kul,

the maximum capacity required is approximately ICOMN/m2.

The cell pressure may change during the test as the rock

specimen defonns and the piston comes into the ceu.

Therefore, a servo-controlled device or a dwnmy piston should

be used to keep the pressure constant, or at least minimize the

pressure change during the test. When oil is used as the cell

pressure medium, or when the cell pressure is adjusted

mechanicauy, a dummy piston with the same diameter as that

of the loading piston should bc used so that it can move

backward in accordance with the forward movement of the

loading piston. Using the dummy piston, one can minimize

the cell pressure change in a triaxial cell. When using a

mechanical means, it is however difficult to allow for the

volumetric change of the rock specimen. According to the

method suggested by the International Society for Rock

Mechanics aSRM)i8), the change in cell pressure during the

test should be less than 1%.

3.5.2 Axial Loading

3.5.2. I Deformation of a Rock Speeimen

There are two methods used to measure the deformation of a

rcck specimen. One method measures the deformation

directly using electrical resistance strain gauges, LDTs, or a

circumferential deformation meter mounted on the specimen.

The other method uses an LVDT or a dial gauge located outside

the specimen. Wbichever is used, it. is essential to adjust

carefuuy the initial point (zero point), the span and the

- 146 -

25

~ 2c z ~:

e' "s:: 15

~:~ ro

" " " I~

c~5 "e

~~ o

- ~o ooo -5 ooo 5 coo ro ooo Tension <-- stram ( x l0-6) ~~> compression

Fignre 5.1 Example oftriaxialcompression tests on Tage-tuff (Got013))

sensitivity, immediately before axial loading is commenced.

When an electrical resistance strain gauge is used, the quality

of bonding greatly influenccs the measurement result. The

gauges must therefore bc attached to the surface of the

specimen very carefuuy. Furthermore, if strain gauges are

used for soft rocks, gauge sensitivity may be decreased by the

rigidity of the gauge base and the resistance element. It is

therefore recommended to select a strain gauge of low rigidity

when testing soft rocks. In addition, for some selected cell

pressure levels, the sensitivity of the strain gauge may be

pressure dependent, and should be exalnined beforehand.

When measuring rock deformation using a device installed

outside the triaxial cell, the axial strain of the rcck specimen

may be overestimated due to the infiuence of a so-called

"bedding error" caused by a loose layer or incorrect end

fmishing of the specimen. Therefore, adjustments may be

necessary, and the results may have to be corrected, depending

600

500

~ ¥ Z ~~ 400

(v

u l:~

(v

(1'

~ ~;5'* 300

~ e;

* " ,,,

~ 200 f:~

O

~ 100

Figure 5.2

on the testing device used.

Figure 5.1 shows principal stress difference･-strain curves

measured by strain gauges. The rock specimen was Tage tuff,

and tests were performed at a ceu pressure of 2MN/m2. The

specimen was 30mm in diameter and 75mm in height, and was

jacketed with snicon rubbcr. The axial loading was controlled

with the displacement transducer installed outside the triaxial

cell. The displacement of the specimen was measured directly

by strain gauges attached longitudinauy and circunferentially

on the surface of the specimen. The two circuuferential strain

gauges were located orthogonauy with rcspect to one another.

The volumetric strain was calculated as the surn of the axial

strain and the twice the circunferential strain readings. The

figure represents the relation between principal stress

difference and axial, circuuferential and volumetric strains.

As shown in the figure, the volumetric strain changed from

compression to dilation at a principal stress difference of about

18MN/m2, and the rock specimen significantly dilated after the

peak principal stress difference was reached. In this test, the

load and strain data were acquired at a sampling rate of one

point per second, the rate high enough to read a continuous

change in the strain variation with stress. It was observed

after the test that a single shear plane had fonned at an angle of

about 35 degrees to the specimen axis. Fortunately, since the

strain gauges happened to be located just off the shear plane,

the strains were measured successfuhy from the beginning to

the end of the test. Had the shear plane formed underneath the

strain gauges, they would have been discomecte(~ and the

measurements would have become impossible from that

moment. This possibility is a disadvantage of using strain

~lOooo -8000 -6coo -2000 2 ooo loooo 4 ooo 6 ooo 8 ooo 4 ooo O

Tension <-- --> Compression Strain (xro-G)

Results of triaxial compression tests on Inada-granite with circumferential measurements (Yamaguchi et al.51))

147

gauges for these measurements.

Figure 5.2 shows the results of triaxial compression tests for

Inada granite under various ceu pressures. The specimen was

50mm in diameter and ICOmm in height. In the test, the

specimen was jacketed with a heat shrinkage tube, and an axial

deformation transducer and chain-type circunferential

deformation transducer were set around the tube. The

specimen was loaded at a constant rate of circumferential

deformation of 0.02mm/min. In the test, the so-caned Class H

behavior was successfuhy obtained under a constant

circuuferential deformation rate after peak stress was reached.

It is generally impossible to obtain C.lass 11 behavior under a

constant axial-strain rate. As shown in this figure, volumetric

strain changed from compression to dilation as principal stress

difference increased, and there was a significant volume

increase in the rock after the peak principal stress difference.

Compared to measurements with strain gauges, measurements

with the displacement transducers are rarely iniluenced by a

localized crack even on rock specimens of Class n type.

Since the complete stress-strain relationship may not be

obtained when displacements or strains are measured locally,

the method for measuring displacement must be chosen taking

into consideration the rock type and its failure mode.

3.5.2.2 Loading Rate

Loading rate may range from a very slow rate of l0-14 s~l

corresponding to the deformation of the earth's crust, to a very

high rate, as in rock blasting with explosives_ It is however

not practical to cover such a wide range of loading rate with a

single testing device. Thus, a loading rate of 0_OI to

0,1 %/min. is usually used, and the ISRMIB) recommends a

loading rate at which the specimen reaches peak strength in 5 to

15min. or from 3 to 60MN/m2/min.

The strength of a rock is influenced by the rate of loading:

the slower the loading rate, the lower the strength. However,

the effect of loading rate on the strength is sman compared to

other factors such as cell pressure. The servo-controlled

testing machines that are, now available enable us to control

loading rate accurately. Furthermore, deformation behavior

after peak strength has now been investigated in detail with a

testing machine with high stiffnese.

3.5.2.3 Fracture Strength and Residual Strength

The difference between failure strength and residual strength

is defined as the stress drop. The index represents the

intensity of the fracture. The smaller the index becomes, the

more ductile the rcck deformation behavior. When the

deformation of the rock specimen becomes ductile, the stress

drop is significantly reduced, and it is sometimes hard to

pinpoint the peak strength. Once the deformation bchavior

changes to a strain hardening type, it may bccome impossible

to determine the peak strength. In that case the strength is

alternatively defined as the stress at a deformation of 2, 3 or 5%.

Figure 5.3 shows how to determine strength-defermation

behavior using stress-strain curves.

In general, the amount of the strain up to failure is caued

"ductility". Handinl6) has classified rock-deformation

behavior using ductility as follows:

Less than 1% very brittle

1 to 5% brittle 2 to 8% moderately brittle (transitionaD

5 to 10% moderately ductile

a

r.r (T

B t

J

l

~

f I ' l l vo

B c

---- f~ I f t

A :~ I

i~ ~ "li l~ c')1 i ~ ci

(T

!.r B

-- A ~d~

El (1)

E LrDL~ILI c (b)

Figure 5.3 Ihterpretation of strength and deformation characteristics from the stress-strain curves

(a) Stress-strain curve of brittle nature

A:yield point, B: failure point. Sy:yield stress, S*:failure stress. Sr:residual stress. E:defounation modulus

(b) Stress-strain curve of transitional nature

B: failure point. C: ductile fanure point, S*:faihre stress, Sb:ductile fanure stress. Du:degree of ductility

(c) Stress-strain curve of typically ductile nature causing strain hardening

B:start of Bnear strain hardening, S*. S2. S3. S5 may bc used as apparent strengths for convemence

- 148 -

More than 10% ductile

The mecbanism of the transition from brittle to ductile is not

yet well understood. Research into this mechanism will be

very important in the future.

3.5.2.4 Loading Control (Strain-Rate Control and Stress-Rate

Control)

There are two ways to control the loading rate: by the strain

rate control or by the stress rate control. Generally, strain-rate

control is used for soft rocks, while both strain-rate and

stress-rate controls are used with similar frequency for hard

rocks .

Although the ISRM18) suggested that testing should be

performed principauy under a constant stress rate, a rock

specimen tested using stress-rate control fractures suddenly

when the stress reaches a maximum value. Thus, the testing

machine is unable to measure the rapid defo~mation of the

specimen beyond peak strength. Therefore, testing under a

constant stress rate may not be appropriate for the purpose of

obtaining a complete stress-strain curve, representing the

deformation behavior from the beginning to some point after

the peak strength. .

On the other hand, the stress rate is not held constant

throughout the test when the strain-rate contr61 method is used.

The strain-rate control method enables us to observe post-peak

deformation bchavior. For strain-rate control method, either

the axial strain rate or a circunferential strain rate can be

controlled. Deformation behavior after the peak strength is

divided into two Classes. They are schematically represented

in Figure 5.4. Class I deformation behavior is typically

strain-softening behavior, while the gradient of stress-strain

curve is positive in the case of Class n bchavior. In general,

using an axial strain-rate control method, it is possible to obtain

a complete stress-strain relationship for rocks displaying Class

T

""

" * ~s

I

I

aas* n !

Class I

I behavior. However, Class n deformation behavior caunot

be obtained using axial strain-rate control, because unstable

failures may occur rapidly after the peak strength is attained.

To obtain a complete stress-strain relationship of Class 11 -type

rocks, a circunferential strain-rate control method is necessary.

3.6 CALCULATIONS OF TEST RESIJliTS

3.6. I Area Correction

The equation of the pdncipal stress difference in the standard

(section 6.2(2)) is computed, assunaing no volume change in

the specimen during thc test (volume cbange AV = O, or

volumetric strain ev = O). This assumption is valid only for

saturated materials with sriffness equal or smaller than that of

soft rocks. For materials with higher stidhless, volulne change

does occur even under undrained condition during axial

compression. The assumption therefore does not hold (Kita et

al.24). In case volumetric strain ev (%) is measured during

axial compression, the principal stress difference (aa a*)

(MNlmz) at the axial strain ea (9ifv) is calculated from the

following equation:

(cia ~cFr)= lOP (1-ea /lOO)

Ao (1-ev/100)

Where the volumetric strain is calculated using either one of

the next two equations:

1) When lateral strain e* is measured:

ev = 8a + 2 e*

2) When volume change AV(cm3) is directly measured

ey = 100 AV/Vo

3.6.2 Correction for the Origin

When the longitudinal displacement of a

~

~~

a;

u c: e'

~ a' ~1 1;:

u' u' a'

c"

~ c:~

v ~~

O~

( (1a ~ (rr) T'ax

I

l

specimen is

ea f

Strain -->

Fignre 5,4 Class I and Classll behaviors (Wavessik & FairhursPo))

Corrected origin Axial strain E. (~)

Figure 6.1 Correction method of origin for stress-strain curves in the

case that an inflection point is included at the initial part of the curve

ovavessik & Faithurs~o))

- 149 -

measured externally, e.g., as a movement of the loading ram,

t.he relationship between principal stress difference and axial

strain becomes in general S-shaped, as shown in Figure 6.1.

One of the reasons for this is bedding error. This is a

measurement error due to incomplete contact between the

specimen end flnished ffat and the loading cap (or the specimen

end and the pedestal) caused by lack of parallelness between

t.he two. The bedding error also occurs when the specimen

ends are somewhat disturbed during sample preparation, and

the thin layer of disturbed rock is compressed unevenly

(Tatsuoka & Kohata46)). As a consequence, the axial strain

given by the external measurement includes an amount coming

from the bcdding error, and measured axial strain is therefore

overestixnated. To exclude bedding error, it is necessary to

perform displacement measurement directly on the side of the

There are however cases where external specimen.

displacement measurements may bc more practical, e.g., when

there is a structural problem in the testing system and intemal

measurement is not possible, or when only the compressive

strength of the material is required. In such cases, the origin

must be corrected, as follows. To obtain the strain at

maximum principal stress diff;erence, linear portion of the

6 Kamonzaki sntstone (cD)

~ ¥ ~:

~: LDT q, *4 ,::

~ e)

~~ I Extenat " a' i~ *i*l *2 15~

~ a,' : o.265 MN/m2 c::*

- Eo : 1 370 MN/m2 G * q~,* : 5.04 MN/m' !~

oo 0.5 1 Axial strain e. (~6)

l.5

Figure 6.2 Example of triaxial tests on siltstone retrieved from

Kazusa Group (Tatsuoka et aL47))

- 12 ~~ Akashi sandstone '+ (T.' =0. 51 MN/m2 ~; ~ lO

/ e' LDT v 8 ¥ External c~ /rf t ,L,

6 T'

~; ¥

'1' ' f L -_ 5 2 ./. " ,~

l:~ / f q~..= g. 39 MN/m2. E0= 1 520 MN/m2 !~

Axialstrain c* (~~)

Figure 6.3 Example of triaxial tests on Akashi sandstone (Kahata et al.26))

S-shaped principal stress difference vs. axial strain curve just

past the infiection point is frst extrapolated in the direction of

the origin. The intersection with the axis of the axial strain is

defined as a new origin. The subsequent axial strains are then

corrected by this amount. This procedure is referred to as

origin correction. As mentioned above, axial strain evaluated

from the external displacement measurement includes an

amount for the bedding error in triaxial compression tests on

stiff materials such as soft and hard rocks. For this reason, a

great care must be taken, since the axial strain at maximum

principal stress difference may still be overestimated even after

the origin correction.

Figure 6.2 shows an example of a drained triaxial

compression test performed on a siltstone retrieved from the

Kazusa Group at the tip of the Miura straight, Kanagawa, Japan

(Tatsuoka et al.47)). Prior to compression, the samples were

isotropicauy consolidated at a cell pressure corresponding to

the in situ vertical stress. In the figure, the principal stress

difference~xial strain relationship by the external

displacement measurement is S-shaped, while that by the LDT

(Local Deformation Transducer, Goto et al.ra) measurement

(internal) is not S-shape(L Similar results of triaxial

compression tests on Akashi sandstone are shown in Figure 6.3

(Kohata et al.26)). in this figure, the principal stress

differencelaxiai strain relationships are S-sbaped, whether the

displacement is measured internally, or externally. This

S-shaped relationship is not due to bedding error, but is

considered a reflection of the true rock property. It is

therefore not necessary to correct origin for the measurement

results on the side of the specinen.

3.7 REPORTlNG OF RESULTS

The strain rate is calculated from the change in axial strain

per unit time obtained from the displacement measurements.

It is commonly deteruined as an average rate in the elastic

deformation stage, where the pdncipal stress difference has a

linear relationship with axial strain near the origin, just afer the

r

o

Figure 7.1 Group ofMohr s clfcles

(T

150

axial loading started.

A Mohr's circle for a specimen can be determined from the

values of major and minor principal stresses. A series of

Mohr's circles are then collected for different values of minor

principal stress, as shown in Figure 7.1. Drawing an envelope

of the circles, cohesion and angle of shear resistance can then

be obtained.

Method to obtain strength parametcrs, cohesion c* and the

tangential angle c*, from the relationship between maximum

principal stress difference and mean stress is as follows. As

shown in Figure 7.2, the maximum shear stress is plotted as

Y-data, while the mean strcss is plotted as X-data. Assuming

the relationship between the two is linear, a straight line is

fitted by the least square method, and the slope and the

Y-intercept are obtained. The strength parameters are then

calculated from these values.

3.7. I Representation and Interpretation of Test Results Clypical

Example Results)

Progressive process in brittle failure observed in a rock

specimen under triaxial compression has been reported by

Brace4) and Blemawski2) and is summarized here from the

microstructure aspects, i.e., with respect to microcrack

behaviors (Figure 7.3).

First Stage: With initial application of the principal stress

difference, inherent cracks and pores begin to close,

producing nonlinear, concave upward stress strain curves.

Second Stage: Stress-strain relationships become linear.

Third Stage: Convex upward on principal stress difference vs.

axial strain relationship up to maximwn principal stress

difference. In this region inherent cracks that closed in

the first stage begin to slide. Strcss induced cracks bcgin

to fonn and open up, Ieading to inelastic volume increase

(dilatancy). Volumetric strain shifts from compression to

expansion, and the pore pressure changes from positive to

negative values, associated with stable increase in crack

propagation and crack coalescence.

Forth Stage: Post-peak stress region. Crack growth becomes

unstable and the cracks become localizod, Ieading to a

macroscopic failure of the specimen.

3.7. I . 1 Iypical Examples of Soft Rock and Artificial Soft Rock

Figure 7.4 shows a typical principal stress difference vs, axial

strain relationship for Tage tuff with uniaxial compression

~

~:~S u'lN ~-b ~~- ~-'

X ,Q :~

sin c*

Cu'COS cu

l

1:,

e ~i

o

Mean stress a. + a ) ( 'f 2

Figure 7.2 Method to determine cu and cu

Figure 7.3 Process ofbuttle failure (Modification of the figure in Paterson36))

>

~ 15 [~~!~:I

Z :~

(, ut: Io

q;

q;

~:'

u? a' a'* 5

~ mj~~

~y oo 1~o 1. 0.4 0.6 0.8 0.2

Axial etrain (%)

Figure 7.4 Stress-strain curve of Tage tuff (Study Committee on UC and TC test methodsl9))

2

~ :~

e;v2

1:'

4'*1

~~

~ oo o.4 o.6 0.8 l~o l.2 '-~J 0.2

Axial strain (~)

Figure 7.5 Stress-strain curve of artificial sofi: rock

(Study Committee on UC and TC test methodsl9))

- 151 -

strength of about lOMN/m2 for a mean stress of 0.49MN/m2.

The axial strain (horizontal axis) is measured on the specimen

surface. The ptincipal stress difference vs. axial strain curve

is concave upward at low stress levels, and becomes ~near at a

stress level half the maximum principal stress difference.

After stress-strain relationship shows the convex upward

portion, the peak stress is reached. The specimen then

experiences macroscopic fracture of brittle failure.

Figure 7.5 shows the principal stress difference vs. axial

strain curve of an artlflcial soft roc~ with an isotropic stress of

0.49MN/m2. For sample preparation of the artificial soft rock

refer to the relevant literaturel9). The axial strain is measured

on the specimen surface in the same way as Tage tuff. The

principal stress difference vs, axial strain exbibits almost linear

relationship up to a stress level half the maximum principal

stress difilerence. After that, the principal stress difference vs.

axial strain curve becomes convex upward, and finally the

maximum stress is reached. In the post-peak stress region, the

specimen behaves in a plastic mamer, and does not show strain

softening.

3.7. 1.2 Typical Example of Hard Rocks

Observations by lbanez & Kronenbergll) are introduced here

as a typical example for shale. The shale comes from the

Wiilcox formation, Louisiana. The specimen is prepared to a

cylinder of 12.4mn in diameter, and 25.4mm in length.

Samples are cored and loaded at three orientations: parallel,

perpendicular and at 45 degrees to bedding. Samples are

sealed with either thin polyolefin shrinkable tube (O.03mm

thick) or lead jacket (0.025mm thick). Axial loads are

measured internauy, with corresponding stresses detennined to

a precision of 0.3MN/m2. Figure 7.6 shows Mohr's envelopcs

with respect to the bedding plane and loading directions. The

conprcssive strengths parallel, perpendiculaJ:, and at 45 degrees

to bcdding are strongly dependent on cen pressure. Mohr's

envelopes are distinctly non-linear and fiiction coefficients

decrease with increasing cell pressure. Figure 7.7 shows

principal stress difference vs. axial strain curves for different

orientations. Strengths of shale samples loaded parallel and

perpendicular to bedding are greater than those for samples

loaded at 45 degrees to bedding. Thus this sbale samples

show a smau but measurable anisotropy. Figure 7-8 shows the

principal stress difference vs. the orientation of bcdding

relationship for Martinsburg slate and shale. Obvious

anisotropy is recognized in the shale.

(a) 200

E ¥ Z :~_ 100

~

(b)

o

crl ~ to Bedding

200

o

8 ¥ Z 100 :~;

~ o

lOO 200

(rl // to Bedding

300

a*

400

(MN/m2) 500 600 700

(c)

o

200

~ ¥ ~; 100 ~:_

o

lOO 200

al at 4S' to Bedding

300

(T*

400 500 (MN/m2)

600 700

T--*~~ -~1 o 300 500 600 700 loo 200 400

a. (MNlm2)

Figure 7.6 Mohr's circles for different loading orientations with respect to bcdding plane (Ibanez & Kronenbergi7))

250

200

8 ~ ~ 150 ~:

e 100

t~

50

o

.~r~~~~~r-~r~~.

,~c /~~ ~~e ~ " ~~L / . / ' / i / /

ll 4' /

: cr~ ~ Bedding

-- - : al // to Bedding .--.~' * -~* -- : (It at45' to Bedding

4

c. (~)

Figure 7.7 Stress-strain curves (Ibanez & Kronenbergn))

700

600

~ 500 ¥ Z ~: - 400 ~7

l 300 t~

200

lOO

D : Martinsburg slate (Donath , 1961) (r. = 200 MN/m2

^ : Wilcox formation shale ,:r * = 250 MN/m2

J J~.

10

o lo ao 30 40 50 60 ?o 80 9e Orientation of bedding to (TI (' )

Flgure 7.8 Relationship of maximum pdncipal stress difference and orientation ofbedding to (~1 (Ibanez & Kronenbergrv))

152

Presented as typical examples for sandstones are the test

results on Ki:machi sandstone from Shimane prefecture, and

- 125.0 ~ ¥ Z ~{_ IC0.0

e'

u r:

G; 75 O h ~ 1::

g' 50^O u~ a'

~ ,,?

(1!,:~ 25.0

~ l:~

~ 0.0

''~. '

CP. PP. -" ' 30 25 -*-r- . -- 30 20 - --c~ : -* ･ 30 15 . - -~:~ *

---- : 30 10 ------- : 30 5 --t-: ~O S ,-~- : 15 S -~~-- : 20 5

: 25 5 (MN/m2)

Figure 7.9

30.0

0.5 l.o 2.0 l.5

Axialstrain (%)

Principal stress difference-axjal straiu curves

on Sanjome andesite (Sato et al.38))

8

z ~_

e,

u ,::

a,~

~:

1:,

U, e,

(1'

F:L

u ::;

~4

20 . o

10.0

o~e

./~r~~~/'r

lr ,~~"

~r

J~-

JHr~~~~ ./ _ ~si~s:~,~F$~,4~

_~;-f'l~w CP,, PP~

-~-~,-*.- : 4 2 --.<h~ ~ : 6 4 ---~~--- : 8 2 --- J---* : 10 2

: ~O 8 --o.- : 10 8

: 10 4

(MN/m2)

o . o o . 20 o . 40 o. 60 1 . oo o , 80

Axial strain (%)

Frgure 7,lO Pdncipal stress difference-axial strajn curves on Kimachi sandstone (Sato et al.33))

- 125.0 ~i~

¥ ~:

~_ 100.0

s'

u F: *a'qJ 75,0

1:'

~ S0.0 (v

~

cl$ 25 O ~~

u 1::

e* O.O -1.

Figure7.11

~ 300 ~ Z

those on Sanjome andesite from Fukushima prefecture (Sato et

al,38)). Experiments were conducted by applying ceu pressure

and pore pressure on the cylindrical specimen, and axial

principal stress difference was increased until the ultimate

strength was attained. Tests were car!ied out with stroke

(displacement) control in the axial direction. Strain rate was

kept constant at 3xl0~5s~1. Figures 7.9 and 7.10 are the

principal stress difference vs. the axial strain curves for the

andesite and the sandstone, respectively. The tangential

Young's modulus decreased with the increase in principal stress

difflerence. The hrger the effective pressure, the greater the

Young's modulus and maximum principal stress difference.

Figures 7.11 and 7.12 are the principal stress difference vs. the

volumetric strain curves for the sandstone and the andesite,

respectively. Though distinct dilatancy is observed in any

condition, the extent of the effect of cell pressure and pore

pressure on dilatancy is not clearly shown. In all the

specimens, the pore pressure is decreased with the increase in

principal stress difference. This phenomenon as well as AE

event count rate confirms the occurrence of stress-induced

microcracks in the specimen. Occurrence of microcracks is

one of the typical behaviors of rocks under the deviatric stress,

as reported in many references .

J'-- --a~~:~ ~~~d.tl,~rlE"

1-..1TO~l' l

1"d-'O- ･･d'

'd'l- "I:p･･ ･-

"Itl"Q1'."tr

+T~'I"C~ ~-Orl.,T'~

CP. PP. :30 z5 :30 ao :30 15 :30 Io : 30 s : Io 5 : 15 5 : 20 5 : 25 5 (MN/m2)

1)'~:*;~;:th':_ .

l9'In

*~~,:

~

¥

oo - o . 75 - o . 50 o . 25 o. o o .25 Volumetric strain (%)

Principal stress difference -vo]umetric strain curves

on Sanjome andesite (Sato et al.33)) .¥

3.7.2 Effect of Strain Control Modes on Strength and

Deformation Characteristics

A servo-controlled testing apparatus givcs options to conduct

tests under any arbitrary control conditions to some extent,

such as axial strain control or circunferential strain control

mode. Here, discussion by Yoshinaka et al.52) wiu be

introducedj in which the differences caused by control modes

have been investigated for Inada granite.

~_

c:ve' 20.0

_e'

1;'

+,Q'*,,, ro.o

,~.*~

p" o.o -o.

Figure 7.12

-~1'*1wlll

(~c*c -Q IF-t ' +1*-4'41~ CP. PP.

: 4 2 ---t'---: 6 4 ---~---: 8 2 +--~~*-* : ~0 Z ~-'~.*-

--4-- : 10 8 --e- : 10 8 -~-- : 10 4

(MN/m2)

lh.

* i

60 0.20 O.o 0.20 - O . 40

Voiurnetric strain (~)

Principal stress di~erence-volumstric strain curves

on Sanjome andesite (Sato et al.38))

3.7.2. I Stress-Strain-Tlme Relationships

Figures 7.13 and 7.14 show the relations between principal

stress difference, strain and elapsed time. The difference

between these figures is the strain component that is under

control; constant axial strain rate for Figure 7. 13 and constant

circunferential strain rate for Figure 7.14_ It can be seen in

Figure 7~13 that the principal stress difference linearly

increases up to a peak value, while the circunferential strain

exhibits a rapid increase when approaching the peak principal

stress difference and then failure occurs. On the other hand,

in Figure 7.14, both the principal stress difference and axial

strain increase almost linearly up to near the peak principal

- 153 -

~ ¥ ~;

~ e,

V ~ q,

* ~,

~ 1:,

~ ~Q,

~ Is ~:~

5 ::

~1

40 o

300

200

100

o

G -2 1

(Cell Pressure

iO MN/m2)

(~.~~:~~~ ~s~c~:,sL

P~~~,~ : / 1~9:d'la¥ st(iln

o.ol

o , 008

o , 006

o , e04

o . c02

o

,~,

!1)

rco 200 300 400 'rime (s)

Figure 7.13 Example ofprincipal stress di~erence-strain-tirne relation for condition of constant axial strain rate (Yoshinaka et al.52))

~;

z :~i

s;

,:*

400

300

200

lOO

o

Q~

G -23

Stress

Axial stram

a'~:e,~s!e~$ s,

~:~,,r'

(Cell pressure 10 MN/m2)

o.ol

o . 008

0.006

0.004

0.002

o

,:

,~ IL

aO

o 50 Ioo Time (s)

Figure 7.14 Example ofprincipal stress dif~erence-strain-titne relation for condition of constant radial strain rate (Yoshinaka et al.52))

(Ceu ~ressure : ro MNlm2)

~ ,¥ ~ ~:

a.

V t::

~

~ ~ ~

{:~

u r:

~

400

300

roo

ioo

e

Radial

--~-: --(:F-':

.-~:

2 x 10-5

2 x lO-6

2 x lO-?

(s~i)

Voiurnetric

Axial

- o . ol - o .005 c o .005 Strain

Figure 7, 15 Example of principal stress djf~erence-strain relation for condition of constant axial strain rate Oeloshiuaka et al,s2))

(Cell pressure : Io MN/nf)

E ¥ ~; ~:

e,

V s::,a,

~:

1:,

~

,1;

':~

V r:

,~

400

300

200

lOO

o

''~~-* :

Radial

--d*-･: -~:)-: '~--:

6 . 6 x lO-5

6 . 5 x 10~6

6.S X lO-1

6 . 5 x lO-~a

(s~1)

Volumetric

Axial

-o.ol -o.005 o.005 strain

Figure 7.16 Example of pdncipal stress difference･strain relation for condition of constant radial strain rate (Yloshiuaka et al,52))

stress difference. Au specimens tested show the common

behavior, where the cell pressure is kept constant of 10MN/m2

in allcases, the axial strain rate was 2.0 X 10~5, 2,0>< 10~; or 2.0

X 104 (s~1) and the circumferential strain rate was 26.5 x lO~5

6.5x 10~, 6.5x 10 or65X 10~ (sl)

3.7.2.2 Stress-Strain Relationships

The principal stress difference-strain relation under constant

axial strain rate is shown in Figure 7. 15 and that under constant

circunferential strain rate, in Figure 7. 16, together with the

volumetric strain calculated based on the axial and

circumferential strains. Below 50% of the failure strength, in

spite of different strain rates, the curves for axiaL

circuuferential and volumetric strains roughly fau on a same

straight line, i.e., Young's modulus and Poisson's ratio can be

regarded independent of strain rate in the range the tests

covered.

3.7.2.3 Comparison of the Elastic Constants Measured under

Different Control Modes

The compaison of Young's modulus measured under

different control modes is made as shown in Figure 7. 17. The

Young's modulus was determined in a strain range of 2 X 104-1

x 10-3 and the correspondent stress level of 12 to 60MN/m2.

It is apparent that the Young's modulus is independent of the

control modes.

Concening Poisson's ratio, in spite of considerable

discrepancies, the effect of the control modes is not remarkable

as shown in Figure 7.18. One of the reasons for the

discrepancy may be the non-linea:ity of the radial strain.

3.7.2.4 Axial Strain-Radial Strain Relationship

Under constant axial strain rate, the axial strain-radial strain

relation after dilatancy outset is dependent on the strain rate, as

shown in Figure 7. 19. The higher the strain rate, the smaller

the radial strain under the same value of the axial strain.

Under constant radial strain rate, as shown in Figure 7.20,

the axial strain-radial strain relation also shows strain rate

dependence, but not in a systematic mamer. Under 10MN/m2

cell pressure, stress-induced microcracks are predominantly

oriented in the axial direction. Under the constant axial strain

rate, as shown in Figure 7.13, the principal stress difference

persistently increases up to the peak value. However, under

the constant radial strain rate, as shown in Figure 7. 14, the

increment of the principal stress difference become smaller

when approaching the peak value. This suggests that under

the constant axial strain rate the energy supplied from external

loading is enough for the microcrack propagation. Whereas

under the constant radial strain rate, the situation is opposite.

154

¥ ~ ~ ~h

ce ~s

o :~

:::

~:~

o ~;

75

70

65

60

55

Inada granite (Ceii pressure : 10 MN.Im2)

o o

o : Constant axial strain rate

･ : Constant circumferentia! strain rate

10-s lo7 I0~6 I0-5 ro-~ Strain rate (s~~)

Relationship between strain rate and Young's modulus (Yoshinaka et al,s2))

a,

V F:S

q,

Q'

~'

c!'q,~)

~l u)~~ '~S~ ~ V r:

~l ((7. ~ (tr) msx

2

Figure 7 . 1 7

~Tangent modulus EL 50 ll

( crs (rr) max / l - -- f --

/ /

/ ////

,/b/:

. j

f /f~A Secant modVlus Es~o

~ l

o ,e

{,:

r:

o

o ~+

o.2s

o.20

O.15

O.lO

O. 05

Inada granite (Cell pressure

o:

o o

o

lO MN/m2)

o a

Constant axia! strain rate

Constant circumferential strain rate

Figure 7 ,, 1 8

o ~ 008

ro~a 10~1 Io~s l0-5 ro-4 Strain rate (s~)

Relationship between strain rate and Poisson's ratio (Yosbinaka et al,s2))

(Cel] pressure : 10 MNlm2) Slow ~--

-~- : 2x lO-s ,-~:~- : 2x lO6

,-~~- : 2x 10~7

(s~)

----i:~ Fast

o Axialstrain E* (."lo)

Flgure 7.2 1 Definition of deforn)ation modulus

strain-radial strain relation behaves in a nonsystematic manner^

o . 006

~:

~'

~iC:!_ O.004

~:: (~~

~,:

o ,, 002

o o . 002 o . 004 o . 006 o . 008 Axial strain

Figure 7.19 ~ial strain-radial strain relation for condition of constant axial strain rate (Yoshirraka et al.52))

l::

,1S

~,?

E1:

~S C~!

~::

o

o . 008

o . 006

o . 004

o . 002

(Cell Pressur~ : 10 MN/m2)

-~- : 6.5 x lO5 ,-~-, : G.5 x lOfi

-{:h-: 6~Sx ~0~7

-~--: 6~5 x lOB

(sl)

o o OOG 0.008 o o~002 o~004 Axta} strain

Figure 7.20 Axial strajn-radial strain relation

for condition of constant radial strain rate (Yoshinaka et al,52))

Therefore due to the obstruction of heterogeneity the

microcracks propagate and stop interrDittently. Thus, the axial

3.7.3 Definition of Deformation Modulus

Definition of the deformation modulus is illustrated in Figure

7.21. In this stan(iard, secant modulus and tangential modulus

are calculated respectively as E~,50 and E~50, for the point on the

principal stress difference vs. axial strain curve at 50% of the

compressive strength, when required. When the test results

with the extemal displacement measurements are used,

deformation modulus is calculated using" the relationship

between principal stress difference and axial strain, which is

corrected for the origin. On the other hand, deformation

modulus is calculated directly from the relationship between

principal stress difference and axial strain, when the

displacement (or strain) is measured on the side of the

specimen. Note that the former case contains measurement

error, and the calculated defomation modulus is therefore

underestimated (e.g., Study Committee on UC and TC test

methods 19)).

Should the flatness and evenness of the specimen ends be

diflilcult to be ensured, it is desirable to apply capping material

like plaster on the top and bottom specimen ends_ It is

reported by Study Committee on UC and TC test methodsl9)

that E*,50 obtained for capped material can be larger than that

for not-capped material, in case displacement is measured

externahy. Test results obtained to date are mostly E~,50 by the

external displacement measurements. in this standard, it is

therefore suggested to obtain Et,5e, if necessary-

Axial strain as in the principal stress difference vs. axial

strain varies, depending upon how the origin is determined.

Consequently, E*,50 calculated as (cF* a,)/8* is affected by the

origin location. On the other hand, the tangential slope at a

certain point on the principal stress difference vs. axial strain

- 155 -

relationship is calculated as d(c* - o*)/d e*, and is not affected

by the location of the origin. In this standard, EL50 is therefore

defined for this reason. Note that thus defined defonnation

modulus too is underestimated for the test data from the

external displacement measurements. In addition, it is

generauy known (Tanaka et al.45)) that deformation modulus is

dependent on strain and pressure levels. In calculating

deformation modulus, it is desirable to state clearly what values

of axial strain and principal stress difference are used.

3.8 A TESTlNG METHOD NOT INCLUDED IN THE

STANDARD (MUL11STAGE TR JAXIAL

COMPRESSION TEST) Starting a triaxial compression test from a low cell pressure,

and repeatedly increasing cell pressures in steps once the axial

stress reaches the maximum value at the selected cell pressure,

it is possible to obtain several Mohr's circles using a single

rock specimen. This procedu:e is caned multistage triaxial

test, and was originally developed by Kovari & Tisa29)

In a conventional triaxial compression test, several

peak-strength and residual-strength measurements are usually

carried out for a single cell pressure. Therefore, the test must

bc conducted under different ceu pressures using two or more

t~

~ ,a,

I~ ~~

1~ ,~ ~;

:~

i:~

~ ~ *X '1!

~:

f

7i t: :

i :! l ~ : ~/ t l

i! j ! I

t

i

p' :+ :

t I l t

~ I , ~ ~ I I Al t ~ 'r ~ l~ I ~ :~ 7t I ~ A tl : ~ ･1~ : i t - cr3 ! t I i~ I l_ , r. 'fl; a t +: ~ ' / ~ j :1 'l / ~/ : ~t t ll I " / l ;~ 'l t :: //J// l

j +t

i 'l + il t'/ / f 1! .11' ~/~ I : .)l

t .1'y

f : ' :pathi * 'i')l

'lll y

'l / /~ / -- : Path2 Minimum principal stress (T3

Figure 8. I Stress path for multistage triaxial test CCjyama et al.25))

specimens to investigate the uiaxial compressive strength

characteristic of the rock Accordingly, it is recommended

that more than four specimens be tested under selected cell

pressures. In contrast, the multistage triaxial test uses only

one specimen to obtain the triaxial compressive strengths under

different cell pressures. It is therefore a very useftil method

for determining the triaxial strength of a rock, especiauy when

very few rock samples can be retrieved from boreholes because

of the poor rock conditions in situ.

The quality of a rock frequently varies in the field, and a rock

may possess different strengths locauy, even if it comes from

the same rock fonnation. Practically, it is very difficult to

obtain unfonn rock samples consistently. It is especially hard

to obtain a sample from the weaker part of a rock formation

with a low RQD, but the strength data for the weak rock may

be the most important for the design and construction of

structures in that rock mass. The multistage triaxial

compression test using only one specimen can bc a helpftil

method for reducing the nuniber of necessary drill holes, as

well as for the accurate and safe design and construction of a

rock structure.

The following problems must be considered in the

application of a triaxial compression test:

1) Strength may bc underestimated due to stress history.

2) The multistage triaxial test is an alternative to the

conventional method.

3) The strength measurement obtained from multistage

triaxial test using a single specimen may or may not be

a valid representation of the strength of the rock

4) A method for judging peak strength has not yet been

established.

5) It is currently hard to control the testing machine at

stresses near the peak strength.

6) Human error in machine operation may generate invalid

data.

3.8.1 Stress Path in a Multistage Triaxial Test

As shown in Figure 8.1, there are two principal stress paths

in a multistage triaxial compression test. In the first, the cell

pressure increases iu steps after axial stress reaches peak

strength (Path 1), and in the second, the cell pressure is

decreased to a hydrostatic state after the peak strengt.h is

reached and before the cell pressure is increased to the next

selected pressure (Path 2). The peak strength for each cell

pressure is defined as the strength at that cell pressure in both

156

~ 160 ~ Z 140 a* = 20 MN/m2 ~: a. = 15 MN/m2 +~q;~ izo

~ 100 a.=10 MN/m2 qJ

~ ~~~3- 80 a*=5MN/m2 " " ~ 60

" 40 ~~ ~~ 20 'T*=3MN/m2 " ,:

1:: o

O 0.5 1.0 1.5 Axialstrain (~)

Figure 8.2 Example of multistage triaxial test on sandstone (Seto et al.40))

Load

Screw

~~ To hydranlic purnp

Pressure chamber

Figure 8.3 Hoek cell

procedures. In the multistage triaxial compression test, axial

loading under maximwn ceu pressure is continued after peak

strength is attained to obtain a complete stress-strain

relationship. The cell pressure is subsequently reduced to a

selected minhnum pressure, and the axial stress is again

increased while maintaiBing that ceu pressure to obtain the

residual strength. Figure 8.2 shows the result obtained on

sandstone from a multistage triaxial compression test using

Path I . The maximum cell pressure was 20MN/m2 in this test.

In the test shown in Figure 8.2, a Hoek-type triaxial cell was

used. The Hoek cell was developed for the tcsting of hard

rocks; it is schematically shown in Figure 8.3. The membrane

(rubber sealing sleeve) used in the Hoek ceu is made from a

relatively hard rubbcr 1-2nnn thick with upper and lower

ffanges. When installing the membrane into the triaxial celL

the membrane is frrst inserted into the cylinder while expande(L

and it is then turned down at far end to make the flange. The

membrane is the most critical element of this cell, and only the

specimens are replaced for the succeeding tests. In ttiaxial

compression tests, the Hoek cdl is mounted on a loading

f rame .

3.8.2 Determination of Peak Strength

Several methods for judging whether or not axial stress has

reached the peak strength have been suggested, but none has

yet bcen accepted as a standard. One proposed method uses

the acoustic emission (AE) count rate to define the poak

strength, when the AE count rate exceeds a predetermined level.

Othor methods set the peak strength at the point when a stress

drop of more tban 0.05MN/m2 is observed or when the ratio of

increase in principal stress difference to that of lateral strain

decreases to a predetermined value.

3.8_3 Examples of Multistage Triaxial Compression Test

In this section, examples for hard and mediwn-hard rocks are

described.

Kovari & Tisa29) tested sandstone and marble under various

cell pressures. The results are shown in Figures 8.4 and 8.5.

As shown in Figure 8 .4, the peak strength is independent of

stress history, and is a function of cell pressure only.

3co

200

E

~; :~ 100

t)

e'

v ~ Oo * "

1:'

~ 300 q,

* " ~~ C~ 200 ~ ~:

~~

Figure 8.4

z;

~~

15

10

5

oo

lOO

1

Axial strain c

2

(%)

3

1

Axiai strain e (~)

Peak strength of sandstone in mlrltistage triaxial test

(Kovari & Tisa29))

A

B 8.82

l.96 3.92

Fignres are cell

Pressures (MNlm2)

?.85B.S6 7.85

5.8S 5.88s~90

9.81

3.92

2.94 1 96

Figure 8.5

2 4 e 7 8 3

Axial strain e (~)

Residual strength of marble in multistage triaxiai test

(Kovari & Tisa29))

i>

- 157 -

Furthermore, as shown in Figure 8.S, the peak strength is also

independsnt of stress history. Therefore, it may be concluded

that the multistage triaxial compression test should bc

applicable for obtaining the peak strength and residual strength

of hard rocks such as sandstone and marble.

On the other hand, Chang & Jumper8) conducted multistage

triaxial compression tests on moderately ductile oily-shale

using three different stress paths. The stress paths used in the

tests are shown in Figure 8.6. For the stress path shown in

Figure 8.6(a), it was very hard to change the cell pressure, and

consistent results were not obtained. However, the test results

with the stress paths shown in Figures 8.6(b) and (c) are

consistent with those obtained using the conventional ttiaxial

tests. Therefore, although various types of stress paths can he

used in a multistage triaxial test, some paths may not bc

suitable for given rock type for consistent results. Akai et al.1)

apphed the multistage triaxial compression test to a very

porous sandy silt (porosity = 54.4 %) with high water content,

w = 489:b. For this soft rock; it was very hard to stop the axial

loading just before peak strength was attained before changing

the cell pressure. The actual procedure employed was to

reduce the axial stress to a hydrostatic state just before peak

strength was reached and then to cbange the cell pressure.

This way, they were able to obtain the consistent results.

Ref erences

q

o : Starting point of test

e : Final point of test

Ultimate strength

f' . ~~~~~~~

.. ,/ Resjdlia~ strength

q

(a) p

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p (c)

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160