lecture4indext4

8/2/2019 lecture4indext4

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Lecture 4 Index properties

Longitudinal Velocity and Degree of Fissuring

Uniaxial Compression

Point Load Strength

Shore Hardness

Schmidt Hardness

Brazilian Test

4-point Beam Test

Uniaxial Tension Test

Rock Quality Designation

Testing Mechanical Properties

1 Uniaxial Compression Tests

Direct test

Load P

Rock cylinder

X-sectionarea = A

Endcap

Strain

Gages E

1Stress

Axial

Strain (1)Lateral

Strain (2)

12=2/1

1

C0 (failure)

C0 : Uniaxial Compressive Strength

E: Modulus of Elasticity

: Poissons RatioAP

Cpeak

o =


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Indirect test (Point LoadTest)

Steel

cones rock

Hydraulic

ram

Testing Mechanical Properties1. Uniaxial Compressive Strength Tests

Measurement of the Point LoadStrength Is and of the indirect C0

A rock core is loaded diametrically between the tips oftwo hardened steel cones, causing failure through thedevelopment of tensile cracks parallel to the loadingdirection.

2

peak

sD

PI =

The load at failure Ppeak is recorded and the pointload strength is calculated from:

where D is the distance between the two cone tips.


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Measurement of the point loadstrength Is and of the indirect C0

The uniaxial compressive strength C0 is then indirectlyobtained by using the empirical relationship:

where Is(50) is the point load strength of 50 mm (2 in.)diameter cores

)50(soI24C =

Testing Mechanical Properties (contd.)

2. Hardness (also used as Indirect Uniaxial CompressiveStrength Tests)

(a) Shore Scleroscope (b) Schmidt Hammer

Rock

specimen

Graduated window showing the rebound of

pellet or spring


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Measurement of the Shore hardness HShore

and the Indirect Determination of C0

Shore hardness (HShore) is measured as the extent ofrebound of a steel bullet dropped from a specificheight onto the surface of a rock specimen.

The harder the rock, the higher the bounce.

An empirical correlation between rock hardness and

its uniaxial compressive strength has been obtainedbased on a large number of tests on different rocks,and is given by:

62.3H)ft/lb(000066.0)psi(ClogShore

3

dryo+=

Measurement of the Schmidt hardnessHSmdt, and the Indirect Determination of C0

The Schmidt Hammer is a portable tool, similar inprinciple to the Shore Scleroscope. It is usedexclusively for rock and rock-like materials and iseasy of use in the field. It measures the rebound offthe surface of rock of a spring-driven steel pellet.

An empirical correlation between the Schmidt rockhardness and uniaxial compressive strength hasbeen obtained based on a large number of tests ondifferent rocks:

16.3H)ft/lb(00014.0)psi(ClogSmdt

3

dry0+=


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Testing Mechanical Properties (contd.)3. Tensile Strength Tests

(a) Brazilian (indirect) Test

Flat

platens

Rock

disk

(a) Measurement of the Brazilian

tensile strength TB

This is an indirect measurement of the tensilestrength of rock.

A rock disk of uniform thickness is cut from a rockcore, and is loaded diametrically between upper andlower flat (or rounded) platens in a compressiontesting machine. Thus, a compressive line-load is

applied to the disk.

When the peak load Ppeak is reached the disk willtypically split along the loaded diameter.


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Theoretical Stresses in Rock during

Brazilian Test

Stress Parallel to load is compressive at the edges and tensile in the middle.

Stress perpendicular to the load is greater but rocks are stronger in compression than

tension so the rock splits in tension.

Measurement of the Braziliantensile strength TB (contd.)

Theoretical analysis shows that uniform tensilestress develops along this diameter. The tensilestrength TB can be obtained from the elasticsolution:

tD

P2T peak

B

=

where Ppeak is the load at failure, t and D are thethickness and diameter of the disk respectively.The ratio of t/D is 1/4 to 1/2.


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L / 3 L / 3 L / 3

P

P / 2 P / 2

D Rock Core

3

peak

MRD3

LP1T

=

(b) Four-point-beam modulus ofrupture (tensile strength) TMR.

In this test a long rock core is flexured to failure. There are

four contacting points dividing the core into three sections ofequal length. The middle section is under pure bending. Themaximum tensile stress occurs in the bottom layer of the

middle section of the core, and this is where failure typicallyoccurs as P reaches Ppeak. This test determines the modulus of

rupture (TMR) (beam flexural tensile strength). From the theoryof beams:

Direct Uniaxial Tension Test Setup

steam/water

actuator

Woods metal

pull

load cell

specimen threaded bolts

Difficult to attach

sample ends and not

bend the sample


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Rock Mass Classifications

Rock Mass Rating (see tables inIntroduction to Rock Mechanics)

Strength of the rock

Drill core quality (RQD)

Groundwater conditions

Joint and fracture spacing

Joint characteristics

Add values from the 5 tables to get total score

Rock Strength


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Rock Quality Designation

Applies to NX core (2.125 diameter)

Hi RQD few fractures in core

Low RQD many fractures in core

MidWest Geosciences

Joint Spacing

Can use drill core, if available

Should consider joint set most

likely to influence work


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Joint Condition

Groundwater Conditions


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Geomechanics Classification of

Rock Masses

0-20Very Poor RockV

21-40Poor RockIV

41-60Fair RockIII

61-80Good RockII

81-100Very Good

Rock

I

RMR Sum of

Ratings from 5

categories

Description of

Rock Mass

Class

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