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Creep of frozen soils

Prof. Jilin Qi

State Key Lab of Frozen Soil Engineering Cold & Arid Regions Env. & Eng. Res. Institute Chinese Academy of Sciences Merger

No.286397

(2)

Vienna: For the extension of the underground line U2 from the first to the second district of Vienna, the underground station Schottenring is constructed with low overburden right

beneath the Danube channel. Because of the low overburden, artificial ground freezing was employed as temporary support and sealing device. (http://www.imws.tuwien.ac.at)

Copenhagen: A pedestrian passage from a new metro station to an existing railway station was constructed underground. Since the existing rail traffic had to continue, the ground was frozen to avoid the

risk of collapse due to excavation of the transfer tunnel.

Artificial Ground Freezing Widely used in Europe

Berlin: unter den Linden Metro Station (2006)

The Netherlands: Artificial Ground Freezing at Sophiaspoortunnel

Soft clay: supporting during excavation; diaphragm wall

(3)

Permafrost distribution

Geographical Conditions

Altitude Latitude

Climate

Temperature Precipitation Wind speed etc.

Environment

Vegetation Geography Water supply etc.

Delft Svalbard

(4)

Permafrost table and Active layer

From Andersland and Ladanyi (1999)

Active layer

Permafrost table

Colder regions Warmer regions

Active layer: depth ranging from tens cm to several metres

(5)

AGENDA

Factors influencing creep of frozen soils

Creep of Warm Frozen Soils: Field Observations State of The Art: Creep Models for Frozen Soils

Our attempts on constitutive modeling

Concluding Remarks

(6)

AGENDA

Factors influencing creep of frozen soils

Creep of Warm Frozen Soils

State of The Art: Creep Models for Frozen Soils Our attempts on constitutive modeling

Concluding Remarks

(7)

Frozen soil displays features very similar to that of unfrozen soil

Strain vs. time

Strain rate vs. time dm

tf

TYPICAL creep curves for frozen soil (Ting 1983)

C REEP CURVES FOR FROZEN SOILS

(8)

From Wu and Ma.

1994

Uniaxial compression Frozen Lanzhou sand

S TRESS DEPENDENCE

0 300 600 900

Time/min

0 2 4 6 8 10 12 14 16 18 20

Temperature -1

1.5 MPa 2.5 MPa 4.5 MPa

Triaxial compression Frozen ISO Standard sand

3=0.5 MPa

-5 oC

Both very much stress dependent.

(9)

S TRAIN RATE DEPENDENCE

From Zhu and Carbee (1984)

-2 oC

Under the same temperature, stress increases with strain rate.

(10)

0 4 8 12 16

0 5 10 15 20 25 30

-2 oC

-5 oC

-10oC

Time / h

Creepstrain/%

FromWu and Ma.

1994

dm vs.

stress

tf vs.

stress

T HERMAL DEPENDENCE

5 MPa

Temperature plays a role similar to load

Minimal strain rate and time to failure all dependent on temperature

(11)

dm/mm.h-1

Water content / %

FromWu and Ma. 1994

1.-0.5oC, 1.4 MPa; 2. -1.0oC, 2.2 MPa;3.-2.0oC, 3.4 MPa

D EPENDENT ON TOTAL WATER CONTENT *

Generally, different water content range, different minimal strain rate development for frozen silty clay (samples from Lanzhou, China)

* Total water content: ice is counted as water together with unfrozen water

(12)

3-4

Solute (Nixon and Lem 1984):

S OLUTE DEPENDENCE

The higher solute content, the larger axial strain under a certain stress level.

(13)

T EMPERATURE & SOLUTE CHANGE UNFROZEN WATER CONTENT

Unfrozen water content plays important roles in mechanical properties of frozen soils

Tm

Warm

Frozen Soils

(14)

AGENDA

Factors influencing creep of frozen soils Creep of Warm Frozen Soils

State of The Art: Creep Models for Frozen Soils Our attempts on constitutive modeling

Concluding Remarks

(15)

Shields et al. (1985): -2.5 and -3.0 C.

Foster et al. (1991): -1 C

Tsytovich(1975): different temperature boundaries for different soils

D EFINE WARM FROZEN SOIL

Constant load and stepped temperature

Material: silty clay (CL) Qinghai-Tibet Plateau Different water content: 40%, 80%, 120%

Constant Loads: 0.1, 0.2 and 0.3 MPa, respectively Temperature steps: -1.5, -1.0, -0.6, -0.5 and -0.3 C (Qi and Zhang, 2008)

Temperature boundary:

Detecting unfrozen water content is rather difficult (NMR) Tend to use mechanical properties

(16)

2E+005 4E+005 6E+005 Time (S) 0

2 4 6 8

Strain(%)

40% - 0.1 MPa Strain vs. Time Temperature vs. Time

-2 -1.5 -1 -0.5

Temperature(C)

-2 -1.6 -1.2 -0.8 -0.4

Temperature ( C) 0

0.001 0.002

Strainrate(h-1 )

40%- 0.1 40%- 0.2 40%- 0.3 80%- 0.1 80%- 0.2 80%- 0.3 120%- 0.1 120%- 0.2 120%- 0.3

0

-1.0 -0.6 C

Strain rate vs. Temperature

like we applied higher loads in oedometer test

(17)

Compressive Coefficient vs. Temperature

Own test

Turning point around: -1 C

0 -2 -4 -6 -8

Temperature ( C) 0

1 2 3

Compressivecoefficient(10-2kPa-1)

Testing results by Zhu et al. (1982)

0 -0.4 -0.8 -1.2 -1.6 -2

Temperature ( C) 0

1 2 3 4

Compressivecoefficient(x10-2kPa-1)

w=40%

w=80%

w=120%

-1 C is defined as the temperature boundary for warm frozen soil for the silty clay we frequently encounter on the plateau.

(18)

Active Layer

Thaw Settlement Frozen Soil

Freeze-Thaw PF Table

Surcharge Load

Settlement of road embankment

Different layers, different physical and mechanical processes

Thaw Settlement Freeze-Thaw

Creep

Creep (Warm)

(19)

-2 0 2 4 Temperature ( C)

16 12 8 4 0

Depth(m)

2001.10.1 2003.10.9

Warmer PF layer

0 100 200 300

Duration (Days)

-0.09 -0.07 -0.05 -0.03 -0.01

Settlements(m)

Location: DK 1136+540 (QT Railway)

PF table Ebkmt Base Ebkmt Surf

Settl. of Warm PF

F IELD OBSERVATION Q INGHAI - TIBET R AILWAY

PF Table stable

(20)

Cap Steel Tube

Lubr. Oil

PVC Tube

Plat

Keep Vertical

Mitigate Friction

Convenience; Protection

Road Surface

No. 4: Nail

Original Surface

Permafrost Table No. 1

No. 2

No. 3

F IELD OBSERVATION Q INGHAI - TIBET H IGHWAY

(21)

Along the highway: 300 km, 10 observation sites, 4500 m a.s.l.

(22)

Beiluhe

Test section

On each site: we obtained total settlement and creep The warmer it is, the more creep occurred.

-0.5 oC

-1.2 oC

(23)

23/47

No.06

No.09 Working Site: Beiluhe field station

(by Dr. Zhang)

L ONG - TERM L OAD TEST

Permafrost zone

Seasonally frozen zone

(24)

24/47

p

Natural Surface

PF Talbe Glove PVC tube

Load plate Grease

Active layer

Permafrost

Natural ground, only cared about creep of frozen layer.

(25)

-3 -2 -1 0 1 2 3 4 5 6 0.00

0.01 0.01 0.02 0.02 0.03 0.03 0.04 0.04

5-8-2009 4-2-2010 6-8-2010 5-2-2011 7-8-2011 6-2-2012 7-8-2012

Temperature()

Settlement(m)

Date

09-1#

09-1#

50 kPa

250 kPa

-2.0 -1.5 -1.0 -0.5 0.0 0.00

0.02

0.04

0.06

0.08

2-7-2006 1-7-2008 1-7-2010 30-6-2012

Temperature()

Settlement(m)

Date

Settlement curve Temperature curve

100 kPa 200 kPa 300 kPa

06-1#

Settlement Temperature

No.06

No.09

(26)

AGENDA

Factors influencing creep of frozen soils Creep of Warm Frozen Soils

State of The Art: Creep Models for Frozen Soils Our attempts on constitutive modeling

Concluding Remarks

(27)

Microscopic view

The theory of rate process Damage creep model

C REEP MODELS FOR FROZEN SOILS

Phenomenological view

Empirical model

Time Hardening Theory

Elementary element based creep model

Model classification based on its scale of representation:

4-1

(28)

The theory of rate process: View deformation as a thermal activation process

= exp exp

Statistical thermodynamics

Activation energy

Equation for rate of deformation

Related studies: Andersland (1967), Assur (1980)

Displacement

Activationenergy Activation energy

C REEP MODELS FROM MICROSCOPIC VIEW _1

A reasonable physical description 4-2

Difficulty: Parameters obtained qualitatively by current testing technology

from Fish 1983

(29)

Thermodynamic constraints

Internal variable (Endochronic time)

Endochronic time theory

Constitutive relationship from Gopal et al. 1985

Definition z and z’

= +

Deviatoric: z

Volumetric:z’

= +

2 2

2

1 1

2 2

2

2 1

d dt

dz z

d dt

dz z

Parameters determined byBazant et al. 1983

1) Strain hardening and softening law;

2) Expansion and contraction 3) Hydrostatic pressure sensibility

Unnecessary to specify a yield surface

Difficulty: Parameters for this theory are too many

C REEP MODELS FROM MICROSCOPIC VIEW _2

Endochronic time theory: irreversible thermodynamic process of dissipative material

4-3

(30)

C REEP MODELS FROM MICROSCOPIC VIEW _2

The damage creep model: damage or recovery of soil structure

Damage mechanics for continuum medium

Damage variable

Creep damage equation

Following thermodynamics; Unique internal variable in frozen soil: ice content

Difficulty: Calibration of Parameters for thermodynamics and damage mechanics

From Miao et al. 1995

CT Damage mechanism

grain orientation; damaged area Ice content

Yield criterion Dissipation potential

= 3

2 + + 9

4-4

(31)

I. Primary creep model (Vyalov, 1966) II. Secondary creep model (Ladanyi,1972) III. Tertiary creep model (?)

Simple structure; conveniently applied in simple engineering analysis (first estimation) 1) Poor versatility; 2) do not reflect internal mechanism

Stress-strain-time

Stress-strain rate-time

1 2

Empirical methods a mathematical description of creep curve

Basic form: Classified by creep stages:

C REEP MODELS FROM PHENOMENOLOGICAL VIEW _1

(32)

Time hardening model

C REEP MODELS FROM PHENOMENOLOGICAL VIEW _2

( , ) ( ) ( )

i

cr

f m t

/ E

0

A

b c

t

Klein and Jessberger (1979) : Stress-strain-time:

a b

t dt

Herzog and Hofer (1981):

Simple; direct

Only available for constant temperature

(33)

4-6

C REEP MODELS FROM PHENOMENOLOGICAL VIEW _3

Elementary creep model: combination of mechanical elements Basic elements:

Typical

Combination:

Elastic Viscous Plastic

Maxwell body Kelvin body

Standard Viscoelastic body

Generalized Bingham body

Reasonable mechanical basis; simple structure; convenient in engineering design

(34)

S UMMARIZATION

Some are too complicated in form, too many

parameters, even impossible to be obtained from conventional tests

Some are lacking mechanism, just mathematical description

Some are difficult to accommodate different thermal or load conditions

We need something

new.

(35)

AGENDA

Factors influencing creep of frozen soils Creep of Warm Frozen Soils

State of The Art: Creep Models for Frozen Soils Our attempts on constitutive modeling

Concluding Remarks

(36)

B ORROW THEORIES FROM UNFROZEN SOILS

Ladanyi (1999): creep of frozen soils is not very much different from that of unfrozen soils

Warm frozen soil is between frozen and unfrozen soils, most

likely closer to unfrozen soils

(37)

After Bjerrum, 1973

—Creep of unfrozen soils based on p

c

/

0 0

'

/ /

' exp

' '

c

ep z

z z z z

z p

k V V V

t

' '

'

B C

e c

p

A C

c exp

c

p p

B

Yin, et al. (1989):

Vermeer and Neher(1999):

(38)

Is there an index in frozen soils similar to p

c

?

Questions

What is its relationship with creep?

If so

How is it possible to apply creep model of

unfrozen soils to frozen soils?

(39)

Looking for such an index Relationship with creep

K0

Compression Frozen

Soil Unfrozen

Soil

Establish a creep model for frozen soils based on this index

Settlement of embankments

Methodology

(40)

Phases Purpose Conditions Samples

1 Prove the existence of an index similar to Pc

Same T

Different d 4

Same d

Different T 4

2 Influence of creep on this index d, T, preload 30

3 Comprehensive analysis Relationship: Creep vs. Pc

Orthogonal design:

d, T, preload, creep time

10

48 creep tests so far

Testing

(41)

In “ln(1+e) lnP” coordinates, there is clearly such an index Pseudo preconsolidation pressure

PPC for frozen soils

1,05 MPa

Stress / kPa Time / Hours

Strain/%

K

0

Test

(42)

PPC increases with the increase in d, then does not change obviously PPC increases linearly with the decrease in temperature

Well reflects the bonding in frozen soils

d/ kN/m3

PPC/kPa

Temperature / C

PPC: Mechanical behavior of frozen soils

PPC/kPa

(43)

Preload 0.815 MPa Preload 1.63 MPa

We are not ready to get a relationship between PPC and temperature, creep time; but we successfully proved the existence of such an index.

When preload is less than original PPC, PPC increases with time

When preload is larger than original PPC, PPC decreases with time

(44)

A N ELEMENT MODEL FOR CREEP OF FROZEN SOIL

The creep model is

1 exp ( ) 0

2 2 2

ij ij ij K

ij

M M K K

S S S G

e t t F

G H G H

1 exp 1 ( ) 0

2 2 2 2

ij ij ij K

ij

M M K K N

S S S G Q

e t t F t F

G H G H H

Instantaneous elastic

Viscous(strain rate approaches

zero)

viscous (strain rate increases with

stress)

Viscoplastic with a yield surface

2 2

3 tan tan

m 2 m

m

F J c

p

Yield criterion(Ma, et al. 1994)

Establishing the model

(Dr. Songhe Wang)

(45)

Only creep of underlying permafrost was considered

Field load test Loading pile Numerical model

100 kPa

Long-term load test

(46)

A simple model for creep of frozen soil might provide a way in engineering analysis.

After implementation of this model,

Thermal state analysis Deformation analysis

Numerical simulation

(47)

A

VISCO

-

HYPOPLASTIC CONSTITUTIVE MODEL FOR FROZEN SOIL

s d

2 2

s

s 1 s 2 s cd 3 s 4 s d

s s

tr[( - ) ]

[tr( - )] ( - ) ( - ) ( - )

tr( - ) tr( - )

c c

c

f f c

c

c

c

c c

2 exp( )

f l

s is static stress, d is dynamic stress.

in which c is the cohesion of frozen soil, f is a scalar function of deformation, fcd is a factor of creep damage.

0

t

d l

t

and are parameters, l is the accumulation of deformation.

Static part

(Dr. Guofang Xu, Prof. Wei Wu)

(48)

2 2 2 2

1 2 cd 3 4 d 1 2

tr[( - ) ]

[tr( - )] ( - ) ( - ) ( - ) tr( )

tr( - ) tr( - )

c c c f f c c c c

c c

2 1

cd

1

t

d

f

t

is a parameter, is Macaulay brackets.

Dynamic part

2 2

d 1 2

tr( )

1 and 2 are parameters, is strain acceleration.

Complete constitutive model - Rate dependent

(49)

C ALIBRATION OF THE CONSTITUTIVE MODEL

When the two linear and nonlinear terms in the static part of the model are abbreviated as L1, L2, N1 and N2, this part can be rewritten as:

s

c

1 1

L (

s

): + c

2

L

2

(

s

): c

3

N

1

(

s

) c

4

N

2

(

s

)

In a conventional triaxial test, owing to ,the above equation can be divided into two scalar equations as follows:

2 3

0

2 2 2 2

1

c L

1 11 1

c L

2 12 3

c N

3 11 1

2

3

c N

4 12 1

2

3

2 2 2 2

3

c L

1 21 1

c L

2 22 3

c N

3 21 1

2

3

c N

4 22 1

2

3

Parameters in the static part

(50)

Owing to the radial stiffness EA3 = EB3 = 0, we have

The parameters ci (i = 1, …, 4) can be obtained by solving the above equation system with respect to the variables ci.

(51)

Parameters and can be obtained from the following expressions:

in which Tref is a reference temperature and can be regarded as -1°C (Zhu and Carbee, 1984).

Parameters 1 and 2 in the dynamical part can only be obtained by fitting the experimental data, as done by Hanes and Inman (1985).

1

1 (T Tref )n

2

( T T

ref

)

n

Parameters and

(52)

V ERIFICATION OF THE CONSTITUTIVE MODEL

Uniaxial compression tests at different loading rates

Compressivestress(kPa)

Stress-strain relationship at different strain rates (Data from Zhu and Carbee, 1984)

(53)

Uniaxial creep tests at different stress levels

0 200 400 600 800 0

4 8 12 16

0 400 800 1200 1600 0

4 8 12 16

0 50 100 150 200 250 0

4 8 12 16

0 10 20 30 40

Time (min) 0

2 4 6 8 10

0 500 1000 1500 2000 2500 0

2 4 6

0 400 800 1200 1600 0

2 4 6

10000 kPa 9000 kPa

8000 kPa 7000 kPa

6000 kPa 3000 kPa

Numerical Experimental

1 10 100 1000

0.01 0.1 1

1 10 100 1000 10000 0.001

0.01 0.1 1

1 10 100 1000

0.01 0.1 1

1 10 100

Time (min) 0.1

1

1 10 100 1000 10000 0.0001

0.001 0.01 0.1

1 10 100 1000 10000 1E-005

0.0001 0.001 0.01 0.1

10000 kPa 9000 kPa

8000 kPa 7000 kPa

6000 kPa 3000 kPa

Numerical Experimental

Creep strain vs. time

(Test data from Orth (1986))

Creep strain rate vs. time

(Test data from Orth (1986))

(54)

C ONCLUDING REMARKS

General features in stress-strain-time curves for frozen are similar to that of unfrozen soils. Warm frozen soil is closer to unfrozen soils.

A warm frozen soil is defined according to mechanical properties. Its creep was successfully observed in situ.

No generally recognized constitutive models are found for

creep of frozen soils. We have tried in different ways.

(55)

A CKNOWLEDGEMENTS

National Natural Science Foundation of China (Nos. 41172253 and 41201064)

The European Community through the program “People” as part of the Industry–Academia Pathways and Partnerships project CREEP (PIAPP-GA-2011-286397).

Chinese Academy of Sciences (100-Young Talents Program granted to Dr. Jilin Qi)

Prof. Wei Wu; Dr. Xiaoliang Yao; Dr. Guofang Xu; Dr. Fan Yu;

Dr. Songhe Wang; Mr. Wei Hu; Ms. Ling Ma

Prof. Hans Pette Jostad and all the CREEP colleagues.

(56)

Thanks for your attention!

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