Effects of Stress Rate on Uniaxial Compressive … of Stress Rate.pdfEffects of Stress Rate on...
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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 11 th International Conference on Mining, Materials and Petroleum Engineering The 7 th International Conference on Earth Resources Technology ASEAN Forum on Clean Coal Technology November 11-13, 2013, Chiang Mai
Transcript of Effects of Stress Rate on Uniaxial Compressive … of Stress Rate.pdfEffects of Stress Rate on...
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).
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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
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Rock Salt Specimens
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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)
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The scope of Testing
Laboratory Testing
Testing under Low Temperature (273 K)
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Laboratory Testing
Testing under Ambient Temperature (303 K)
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Laboratory Testing
Testing under High Temperature (343 and 373 K)
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Laboratory Testing
Post-tested specimens
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Test Results
Temperature
(K)
373
343
303
273
¶1/¶t (MPa/s)
0.1 0.01 0.001 0.0001
(0C)
(30C)
(70C)
(100C)
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Loading Rate Uniaxial compressive Strength
Temperature Uniaxial compressive Strength
Test Results
Stress – Strain Curves
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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
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/
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
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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
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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
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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…
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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
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c
c c t expT
Salt Deformation… Strength Criterion
Substituting equations (6) and (7) into (5) we
obtain :
(8)
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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
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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
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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
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Strength Criterion
Octahedral Shear Stress – Strain
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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
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Strength Criterion
E = -0.145T + 69.20
G = -0.054T + 25.82
n = (210-4)T + 0.26
Elastic Modulus vs. Temperature
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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
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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)
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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
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d mW W
Strength Criterion
Distortional vs. Mean Strain Energy
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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).
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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.
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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
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Discussions and Conclusions
Acknowledgements
Funded by Suranaree University of Technology
and by the Higher Education Promotion and National Research University of Thailand
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