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Effects of Stress Rate on Uniaxial

Compressive Strength of Rock Salt

under 0-100C

S. Sartkaew

K. Fuenkajorn

Geomechanics Research Unit

Institute of Engineering

Suranaree University of Technology, Thailand

The 11th International Conference on Mining, Materials and Petroleum Engineering

The 7th International Conference on Earth Resources Technology

ASEAN Forum on Clean Coal Technology

November 11-13, 2013, Chiang Mai

Background and Rationale

Objectives

Rock Salt Specimens

Laboratory Testing

Test Results

Strength Criterion

Discussions and Conclusions

Outline

2

Background and Rationale

3

Northeast

www.thailand-map.net

4

http://www.scotland.gov.uk

Background and Rationale

5 http://www.bine.info

Compressed air energy storage power plant (CAES)

MacIntosh, U.S.A (1991) Huntorf, Germany (1978)

Background and Rationale

6 http://www.gaelectric.ie

The loading rate affects on the compressive

strength and deformability of intact rocks

(Kumar, 1968; Jaeger et al., 2007; Cristescu and

Hunsche, 1998; Albertin et al., 1999).

The strength of salt increases with applied stress

and strain rate (Fuenkajorn et al., 2012; Liang et

al., 2011; Hamami, 1999 and Lajtai et al., 1991).

The rock strength and elastic properties

decrease as temperature increase. (Sriapai et

al., 2012).

7

Background and Rationale

Objectives

Determine the effect of loading rate and

temperature on the compressive strength and

deformability of rock salt

Derive strength criterion as affected by loading

rate and temperature

The stain energy density criterion is proposed to describe the salt strength

8

Rock Salt Specimens

9

Uniaxial compression tests performed under

constant loading rates and temperature

Stress rates (1/t) : 0.0001, 0.001, 0.01 to

0.1 MPa/s

Temperature : 273, 303, 343 and 373 Kelvin

(0, 30, 70 and 100C)

10

The scope of Testing

Laboratory Testing

Testing under Low Temperature (273 K)

11

Laboratory Testing

Testing under Ambient Temperature (303 K)

12

Laboratory Testing

Testing under High Temperature (343 and 373 K)

13

Laboratory Testing

Post-tested specimens

14

Test Results

Temperature

(K)

373

343

303

273

¶1/¶t (MPa/s)

0.1 0.01 0.001 0.0001

(0C)

(30C)

(70C)

(100C)

15

Loading Rate Uniaxial compressive Strength

Temperature Uniaxial compressive Strength

Test Results

Stress – Strain Curves

16

Test Results

1v

2

T= 273 Kelvin = 0.1 MPa/s∂t

∂1

-200 -100 0 100 200

10

20

30

40

1 (MPa)

milli-strains

1v

2

T= 273 Kelvin = 0.001 MPa/s∂t

∂1

-200 -100 0 100 200

10

20

30

40

1 (MPa)

milli-strains

1

v

2

-200 -100 0 100 200

T= 303 Kelvin = 0.1 MPa/s∂t

∂1

10

20

30

40

1 (MPa)

milli-strains

1v

2

-200 -100 0 100 200

T= 303 Kelvin = 0.001 MPa/s∂t

∂1

10

20

30

40

1 (MPa)

milli-strains

1v

2

milli-strains

-200 -100 0 100 200

T= 373 Kelvin = 0.1 MPa/s∂t

∂1

10

20

30

40

1 (MPa)

1

v

2

milli-strains

-200 -100 0 100 200

T= 373 Kelvin = 0.001 MPa/s∂t

∂1

10

20

30

40

1 (MPa)

0C 30C 100C

The mean stresses (m) and strains (m) and

octahedral shear stresses (toct,f) and shear

strains (goct,f) at failure are determined by (Jaeger

et al., 2007):

(1)

(2)

(3)

(4)

Strength Criterion

17

/

oct,f / t

1 22 221 2 1 3 2 31 3

/

oct,f / g

1 22 221 2 1 3 2 31 3

m / 1 2 3 3

m / 1 2 3 3

Octahedral Shear Stress – Strain Curves

18

Strength Criterion

373 343

T= 273 Kelvin303

0 50 100 150 200

t oc

t (M

Pa)

0

5

10

15

20

= 0.1 MPa/s∂t

∂1

goct (milli-strains)

373 343

303 T= 273 Kelvin

0 50 100 150 200

t oc

t (M

Pa)

0

5

10

15

20

= 0.01 MPa/s∂t

∂1

goct (milli-strains)

373 343

303 T= 273 Kelvin

0 50 100 150 200

goct (milli-strains)

t oc

t (M

Pa

)

0

5

10

15

20

= 0.001 MPa/s∂t

∂1

0 50 100 150 200

goct (milli-strains)

t oc

t (M

Pa

)

0

5

10

15

20

= 0.0001 MPa/s∂t

∂1

373 343

303 T= 273 Kelvin

Octahedral Shear Strength vs. Mean Stress

19

Strength Criterion

toct,f = 1.412·m + 0.022 (MPa)

m (MPa)

0 5 10 15 20

t oc

t,f

(M

Pa)

0

5

10

15

20

Temperature (K)

273

303

343

373

Salt Deformation

The total compressive strain is composed of two

component (Jaeger et al., 2007):

(5)

where = Elastic strain

= Plastic creep strain

20

e c

c c c

e

c

c

c

Strength Criterion

The elastic strain can be calculated by (Jaeger

et al., 2007).

(6)

where = Compressive stress

E = Elastic modulus

Salt Deformation…

21

c cc

E

c

Strength Criterion

The exponential creep law is used to describe

time-dependent strain of the salt (Yang et al.,

1999):

(7)

where = Stress constant

= Stress exponent

= Time exponent

= Temperature constant

T = Absolute temperature

22

c

c c t expT

Salt Deformation… Strength Criterion

Substituting equations (6) and (7) into (5) we

obtain :

(8)

23

Salt Deformation…

cc c t exp

E T

Strength Criterion

The creep parameters can be derived in the

forms of the octahedral shear strain:

(9)

where = octahedral shear strain

= octahedral shear stress

G = shear modulus

= temperature constant

24

Salt Deformation…

octg

octt

octoct oct

Gt exp

T

t g t

2

Strength Criterion

For the stress-rate controlled condition the

octahedral shear stress at any loading time (t)

can be expressed as:

(10)

Assuming that the salt elasticity varies linear

with temperature (Fuenkajorn, 2012) :

G = T + G0 (11)

where G0 = Shear modulus at 0 K. 25

Salt Deformation… Strength Criterion

octoct oct

G(t) exp t

T

t g t

2

Substitute equation (11) into (10) we obtain:

(12)

where = octahedral shear stresses rate

, G0, , , , are empirical constants

26

Salt Deformation… Strength Criterion

oct

oct octT G

t(t) t exp

T

t g t

02

octt

Summary of Calibration

Parameters Values R2

-54.04

0.967

G0 25.82

0.01

2.018

0.129

1559.24

27

Strength Criterion

Octahedral Shear Stress – Strain

28

Strength Criterion

373 343

T= 273 Kelvin303

0 50 100 150 200

t oc

t (M

Pa)

0

5

10

15

20

= 0.1 MPa/s∂t

∂1

goct (milli-strains)

373 343

303 T= 273 Kelvin

0 50 100 150 200

t oc

t (M

Pa)

0

5

10

15

20

= 0.01 MPa/s∂t

∂1

goct (milli-strains)

373 343

303 T= 273 Kelvin

0 50 100 150 200

goct (milli-strains)

t oc

t (M

Pa

)

0

5

10

15

20

= 0.001 MPa/s∂t

∂1

0 50 100 150 200

goct (milli-strains)

t oc

t (M

Pa

)

0

5

10

15

20

= 0.0001 MPa/s∂t

∂1

373 343 303

T= 273 Kelvin

Empirical Equation of Elastic Parameter

GPa (13)

GPa (14)

(15)

where E = Elastic Modulus

G = Shear Modulus

n = Poisson’s ratio

T = Temperature

29

Strength Criterion

E = -0.145T + 69.20

G = -0.054T + 25.82

n = (210-4)T + 0.26

Elastic Modulus vs. Temperature

30

E decreases with temperature

E = 15 - 29 GPa

E (

GP

a)

T (Kelvin)

0 250 300 350 400

0

10

20

30

40

E = -0.145T + 69.20 (GPa)

Strength Criterion

Shear Modulus vs. Temperature

31

G decreases with temperature

G = 5 - 11 GPa

0

2

4

6

8

10

12

G (

GP

a)

T (Kelvin)0 250 300 350 400

G = -0.054T + 25.82 (GPa)

Strength Criterion

Poisson’s Ratio vs. Temperature

Independent of loading rate and temperature 32

Poisson’s Ratio = 0.32 - 0.35

n

T (Kelvin)

0 250 300 350 400

0

0.1

0.2

0.3

0.4

0.5

n = (2¶10-4

)T + 0.26

Strength Criterion

Strain Energy Density

Distortional strain energy at failure (Wd) can be

calculated from the octahedral shear stresses

and strains (Jaeger & Cook, 1979):

(13)

Mean strain energy at failure (Wm) calculated

from the mean stresses and strains:

(14)

33

d oct oct/W t g3 2

m m m/W 3 2

Strength Criterion

Strain Energy Density Criterion

Distortional strain energy at failure (Wd) can be

derived as a function of the mean strain energy

density at failure (Wm):

(15)

where and are empirical constant

34

d mW W

Strength Criterion

Distortional vs. Mean Strain Energy

35

Strength Criterion

0 0.5 1 1.5 2 2.5 3

Wm (MPa)

Wd = 1.36·Wm - 0.02

0

0.5

1

2

2.5

3W

d (

MP

a)

1.5

T= 273 K

303

0.01

0.001

0.0001

¶1/¶t

0.1 MPa/s343

373

Discussions and Conclusions

The decrease of the salt strength as the

temperature increases suggests that the applied

thermal energy before the mechanical testing

makes the salt weaker, and more plastic.

The failure stresses increase with the loading

rates, these agree with the experimental results

by Fuenkajorn et al. (2012) and Dubey and

Gairola (2005).

36

The elastic and shear modulus linearly decrease

with increasing temperature. The Poisson’s ratio

however tends to be independent of the

temperature.

For the same temperature the strain increases

with low loading rate. For the same loading rate,

the strains increase with increasing temperature.

37

Discussions and Conclusions

The exponential creep law agrees with the test

results in terms of the octahedral shear strains

as a function of time

The distortion strain energy criterion can be

describe the salt strength under varied stress

rates and temperatures

The criterion can be used to determine the

stability of rock salt around compressed-air or

gas storage cavern

38

Discussions and Conclusions

Acknowledgements

Funded by Suranaree University of Technology

and by the Higher Education Promotion and National Research University of Thailand

39

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