Rock Mechanics- Ch 4

Front 1

Types of triaxial test

Back 1

- Consolidated-undrained test (Cu) - Consolidation-drained test (CDl - Unconsolidated- undrained test(UU)

Front 2

CU/CD/UU test

Back 2

CU - Consolidated undrained triaxial compression tests In a 'consolidated undrained' test the sample is not allowed to drain and the sample is assumed to be fully saturated

- CD In a 'consolidated drained' test the sample is consolidated and the pore presure is allowed to dissipate.

*- UU In an 'unconsolidated undrained' test the loads are applied quickly, and the sample is not allowed to consolidate during the test.

Front 3

Uniaxial Compression test

Back 3

Key points for procedure :

1).Prepare the rock samples ----cylinder of length to diameter ratio inthe range 2 ~2.5Attention:The ends of rock specimen should be flat, smooth and parallelThe ends cut perpendicularly to the cylinder axis

2) Increase the axial pressure (sigma),the stress (sigma) can produce distortion and destruction of rocks

3)After the growth of cracks, the rock reach the peak strength and the test stop.

Front 4

What factors can influence the test result ?

Back 4

Material

Front 5

Deviatoric & Non-deviatoric

Back 5

1.deviatoric stresses (𝜎dev)the normal and shear stresses that remain after subtracting a hydrostatic stress from each normal stress component

2.non deviatoric stresses (𝜎mean)

compressions equally applied in all directions, i.e., hydrostatic state of stress

Deviatoric stress produces distortion and destruction of rocks while non deviatoric stresses generally do not

Front 6

Triaxial compression test

Back 6

Key points for procedure :

 Increase the axial pressure and confining pressure at the same time, make sigma1=sigma2=sigma3,the state we called hydrostatic state and the stress we called non-deviatoric stresses(which were equally applied in all directions and can not producedeformation)

 When the confining pressure reach the limit we settled, keep it as a constant ,that issigma2=sigma3=p.

 Continue to increase the axial pressure (sigma1＞sigma3),the stress (sigma1-sigma3) wecalled deviatoric stress, which can produce distortion and destruction of rocks

 After the growth of cracks, the rock reach the peak strength and the test stop.

Front 7

Triaxial compression test

Back 7

Key points for procedure :

 Increase the axial pressure and confining pressure at the same time, make sigma1=sigma2=sigma3,the state we called hydrostatic state and the stress we called non-deviatoric stresses(which were equally applied in all directions and can not producedeformation)

 When the confining pressure reach the limit we settled, keep it as a constant ,that issigma2=sigma3=p.

 Continue to increase the axial pressure (sigma1＞sigma3),the stress (sigma1-sigma3) wecalled deviatoric stress, which can produce distortion and destruction of rocks

 After the growth of cracks, the rock reach the peak strength and the test stop.

Front 8

Mathematically

Back 8

For a triaxial compression test

• longitudinal strain 𝜀𝑎𝑥ial= Δ𝑙 𝑙 (𝑙: length of rock)

• lateral strain 𝜀lateral= Δ𝑑 𝑑 (𝑑: diameter of rock)

• 𝜀lateral= −𝜈𝜀𝑎𝑥ial(𝜈: Poisson’s ratio)

For linearly elastic and isotropic rocks:

0 < 𝜈 < 0.5; 𝜈 often assumed to be 0.25

• the volume change per unit volume:

Δ𝑉𝑉 = 2𝜀𝑚𝑎𝑡𝑓𝑟𝑎𝑚+ 𝜀𝑎𝑥𝑖𝑎𝑚= 𝜀𝑎𝑥𝑖𝑎𝑚(1 − 2𝜈)

Front 9

Analysis of the Stress-strain curve of uniaxial test

Back 9

OA - Pore fracture compaction stage

AB - Elastic deformation stage

BC - Stable/steady development stage of micro crack

CD - Non-steady/unstable fracture development stage

After D: Post-fracture stage

Front 10

Normal, shear and principal stress

Back 10

What’s normal stress σn?

The stress which is perpendicular to the failure plane

 What’s shear stress τ ?

The stress which is parallel to the failure plane

What’s principle stress ?

The stress , exist on the plane where there is no shear stress at the same time

and the direction of the stress called principle stress orientation

Front 11

Failure Criterion

Back 11

The variation of peak stress 𝜎1 with confining pressure 𝜎3

Front 12

peak shear stress or shear strength

Back 12

The peak shear stress or shear strength 𝝉𝒑= 𝑺𝒊+ 𝝈𝐭𝐚𝐧𝝓𝜙 is called the angle of internal friction; it describes the rate of increase of peak strength with normal stress.

𝑆𝑖: parameter known as cohesion

Eqn=

So ,we can get the angle of fracture(a) plane and the maximum principal stress

𝜙 is the of internal friction angle, so we always find that the angles of fracture plane and the end the specimen are similar and almost greater than 45 °

Front 13

The influence factors of rock properties

Back 13

The size effect

The shape effect

The loading conditions

The environmental effects

Hint 13

S S L E

Front 14

The size effect

Back 14

 The same shape and the ratio of length to diameter is kept constant.

 The compressive strength and brittleness are reduced for larger specimens.

 The elastic modulus does not vary significantly with specimen size

The larger the specimen, the greater the number of micro-cracks and the greater thelikelihood of more severe flaw

Front 15

The shape effect

Back 15

 The size (volume )of specimen is preserved but its shape changes

 The compressive strength and ductility are increased as the aspect ratio

 The elastic modulus is basically unaffected by specimen shape

Use empirical formula to account for the shape effect

Front 16

Loading conditions

Back 16

 The effect of confining pressure applied to the specimen is quite pronounced

 The most brittle behavior is experienced at zero confining pressure.and less brittle behavior as the confining pressure is gradually increased

Front 17

Environmental affects

Back 17

 Moisture content

 Time-dependent effects

 Temperature effects