A Viscous Continuum Mechanics Approach - NAFEMS · A Viscous Continuum Mechanics Approach H....

4th FENet Annual Industry Meeting Lisbon Dec. 2004

Modelling the Swelling Phenomenon of Soils

A Viscous Continuum MechanicsApproach

H. HeidkampC. Katz


Contents

Swelling – essential characteristics

Constitutive modelling Final state relationTime-dependant extensionAlgorithmic aspects

Numerical studies

Conclusive remarks



Construction interferes chemical/ physical balanceLocal unloading of soil domain

Adsorption of water inbetween the layers of clay minerals (osmotic swelling)Chemical transition of anhydrite contents into gypsum

Initiation of a time-dependant swelling process(expansion of soil)


Swelling – practical impact

Expansion of soil is limited by support structures(e.g. tunnel lining)

Generation of significant swelling pressures


Swelling – practical impact

Structural damage due to extensive compressive stresses

Decrease of serviceability


Constitutive modelling


Constitutive modelling

Requirements from practice:

Estimation of the swelling strains/ stresses thatare to be expected

Few „basic“ parameters that can be calibrated from in-situ and laboratory measurements

Accounting for time effect → swelling strain evolution

3D

...


Constitutive modelling ( t = ∞ )

From load controlled oedometer tests (Huder & Amberg):

1D logarithmic relationship between stress and final swelling strain (Grob 1972)

Extension to 3D (Wittke-Gattermann 1998, Kiehl 1990):

„Principal swelling strains essentially depend onthe principal normal stress“



( )( )

0

0 0

0

0 ,log / ,log / ,

i iq

i q i i i i c

c i i c

kσ σ

ε σ σ σ σ σσ σ σ σ

∞

⎧ ≤⎪= − ⋅ < <⎨⎪ ≥⎩

0,00,1

0,20,30,40,5

0,60,70,8

0,91,0

-800 -700 -600 -500 -400 -300 -200 -100 0 100 200

σ [kN/m2]

εq [%]Grob (eq. 2)Test dataUpper Limit

σ0

kq = 0,33%

σc = -2 kN/m2

i = 1..3

measure for magnitude of decompression

summarizes the swelling characteristics of the soil



( )( )

0

0 0

0

0 ,log / ,log / ,

i iq

i q i i i i c

c i i c

kσ σ

ε σ σ σ σ σσ σ σ σ

∞

⎧ ≤⎪= − ⋅ < <⎨⎪ ≥⎩

0,00,1

0,20,30,40,5

0,60,70,8

0,91,0

-800 -700 -600 -500 -400 -300 -200 -100 0 100 200

σ [kN/m2]

εq [%]Grob (eq. 2)Test dataUpper Limit

σ0

kq = 0,33%

σc = -2 kN/m2

i = 1..3


Constitutive modelling ( t < ∞ )

Basic idea illustrated by means of a rheological model

1

E

σ

η

y

σσ

kq

E

η σσ

Parallel coupling of “swelling“ and dashpotdevice


Constitutive modelling ( t < ∞ )

Time dependency via a formal viscous approach

( ), q q q⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠

∞= −φ σ ε ε σ ε

Vector valued creep function ϕ

, qq η

⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠=

φ σ εε&

Define the rate of swelling strains as

with the retardation time η


Constitutive modelling - Algorithm

Displacement FEM framework with incremental(time stepping) global solution strategy

σ∆ ⇒ ∆ε

e q plt t t q pl

⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠

+∆

∆ =∆ +∆ +∆

= − +∆ +∆

ε ε ε ε

C σ σ ε ε

Additive strain decomposition

Integrate swelling strain rates over time increment → backward-Euler approach

1 1, ,t t

t tq q qt

d tτη η⎛ ⎞⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

+∆+∆∆ = ≈ ⋅∆∫ε φ σ ε φ σ ε



Set of 9 nonlinear equations in the 6+3 unknowns

Solved by linearization → Newton-Raphson update scheme

q∆εt tσ+∆ and

k

qq k

kt

δ

η δ∞

⎛ ⎞⎜ ⎟⎝ ⎠

=

∂− +

∂ ∆

C I σ R

εI ε r

σ

( ) ( ),t t t t tq q pl

+∆ +∆∆ = ∆ − − − ∆ − ∆R σ ε ε C σ σ ε ε

1 1;

kq q qk k k k

δ δ+ += + ∆ = ∆ +σ σ σ ε ε ε

( ) ( ), ,t t t tq q qt

η+∆ +∆∆ = − + ⋅ ∆∆

r σ ε φ σ ε ε

Heidkamp, H. & Katz, C. 2002. Soils with swelling potential - Proposal of a final state formulation within an implicit integration scheme and illustrative FE-calculations. Eds.: H.A. Mang, F.G. Rammerstorfer, J. Eberhardsteiner. Proceedings of the 5th

World Congress on Computational Mechanics, Vienna, Austria.

Heidkamp, H. & Katz, C. 2004. The swelling phenomenon of soils – Proposal of an efficient continuum modelling approach.Ed.: W. Schubert. Proceedings of the EUROCK 2004 & 53rd Geomechanics Colloqium, Salzburg, Austria.


Numerical studies


Numerical studies – 1D example

One dimensional case: Unloading under constant stress conditions

Time < 0loading

Time = 0unloading

Time = tswelling strain

evolution


Numerical studies – 1D example

From previous developments, the analytical solution can be derived as

( )

( )0

0

1

tq q

tq q

t d

d

ε ε τ

ε ε τη∞

=

= −

∫

∫

&

( ) 1t

q qt e ηε ε⎛ ⎞⎜ ⎟⋅⎜ ⎟⎝ ⎠

−∞= −

: Axiale Quelldehnung, eta=100 h : Axiale Quelldehnung (analyt.)

: Axiale Quelldehnung, eta=1000 h : Axiale Quelldehnung (analyt.)

Time [h]0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

Swelling Strain [0/00]

0

2

4

6

8

10

( ) ( )0log / 1q

tq qt k e η

ε

ε σ σ∞

⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠

−= − ⋅ ⋅ −14444244443

identical to the 1D relation proposed by Kiehl (1990) for description of the swelling strain evolution


Numerical studies – Calibration

Swelling modulus - Fit to oedometric test data on Caneva Stiff Clay

Oedometric testing (Huder-Amberg)of Caneva stiff clay

0

1

2

3

4

5

6

-800 -700 -600 -500 -400 -300 -200 -100 0

Axial stress [kN/m²]

Axi

al s

wel

ling

stra

in [%

]

Test data EDO7 [Barla 2004]

Test data EDO8 [Barla 2004]

SWEL calibrated: Kq=3,10 [%]

SWEL calibrated: Kq=0,88 [%]

Test-data taken from:Barla, M. 1999. Tunnels in Swelling Ground – Simulation of 3D Stress Paths by Triaxial Laboratory Testing. PhD Thesis, Politecnico di Torino, Italy.


Numerical studies – Calibration

Time dependent swelling evolution - Fit to triaxial test data on Caneva Stiff Clay

Time dependent swelling evolution upon triaxial shear loading

0,00

0,10

0,20

0,30

0,40

0,50

0,60

0,70

0,80

0,90

0 1000 2000 3000 4000 5000 6000 7000 8000

Time [min]

Volu

met

ric s

wel

ling

stra

in [%

]

Triaxial Test Data CNV3 [Barla 2004]

SWEL calibrated: Kq=2,80 [%], Retardation Time=26 [h]

SWEL calibrated: Kq=2,70 [%], Retardation Time=20 [h]

Test-data taken from:Barla, M. 1999. Tunnels in Swelling Ground – Simulation of 3D Stress Paths by Triaxial Laboratory Testing. PhD Thesis, Politecnico di Torino, Italy.


Numerical studies – Engineering ex.

2D FEM simulation of high-speed railway track in swellable soil

Swellable Clay

Sand

Rock

Monitoring of heaving due to swelling

Relalistic background: Construction of high speed railway track Nuremberg – Ingolstadt, GermanyWolffersdorff v., P.A. & Rosner, S. & Wegerer, P. 2004. Planung von bautechnischen Lösungen in den quellgefährdeten Einschnittender Hochgeschwindigkeitsstrecke Nürnberg – Ingolstadt. 28. Baugrundtagung der DGGT in Leipzig.



1st excavation step, ∆t = 2 a

Time dependent heavings due to swelling

0,00

5,00

10,00

15,00

20,00

25,00

30,00

35,00

0 5 10 15 20 25

Time [years]

Hea

ving

s du

e to

sw

ellin

g [m

m]



2nd excavation step , ∆t = 0.5 a


0,00

5,00

10,00

15,00

20,00

25,00

30,00

35,00

0 5 10 15 20 25

Time [years]

Hea

ving

s du

e to

sw

ellin

g [m

m]


0,00

5,00

10,00

15,00

20,00

25,00

30,00

35,00

0 5 10 15 20 25

Time [years]

Hea

ving

s du

e to

sw

ellin

g [m

m]



Soil exchange, ∆t = 1 a


0,00

5,00

10,00

15,00

20,00

25,00

30,00

35,00

0 5 10 15 20 25

Time [years]

Hea

ving

s du

e to

sw

ellin

g [m

m]



Installation of superstructure , ∆t = 0.5 a


0,00

5,00

10,00

15,00

20,00

25,00

30,00

35,00

0 5 10 15 20 25

Time [years]

Hea

ving

s du

e to

sw

ellin

g [m

m]



Remaining heaving, ∆t → ∞


0,00

5,00

10,00

15,00

20,00

25,00

30,00

35,00

0 5 10 15 20 25

Time [years]

Hea

ving

s du

e to

sw

ellin

g [m

m]



2D evolution of the volumetric swelling strain


Conclusive remarks


Conclusive remarks

Engineering design: Importance of appropriate considerationof swelling phenomena

Based on a 3D extension of Grob‘s swelling law: Proposal of an implicit formulation within a viscous framework → accounting for time dependency

Two essential material parameters:→ kq representing the swelling potential→ η modelling the time evolution

Model can be calibrated according to test data → test data is, however, often significantly scattered → rises issue of safety assessment

Applicability to practical engineering problems


Thank you for your attention.Questions?

[email protected]


Finite-Element simulationsLoading of the concrete lining with evolving swelling process

M 1 : 100

XYZ

24.3

24.222.3

22.117.9

17.7

-16.1-15

.9

10.610.5

-8.03

-6.86-4.45

1.97

1.941.93 1.781.75

1.631.53

1.05

-0.734

0.717

0.714

0.641

-0.502

0.438

0.376

Sector of system Beams Group 1 2Beam bending moment My, nonlinear Loadcase 5 PHASE III: Innerlining, 1 cm spacious = 1500. kNm (Min=-16.1) (Max=24.3)

-4.00 -2.00 0.00 2.00 4.00 6.00 m

12.00

10.00

8.00

6.00

4.00

2.00

0.00

-2.00

M 1 : 100

XYZ

Sector of system Beams Group 1 2Deformed Structure from LC 104 MAX-VY Enlarged by 130.0

-4.00 -2.00 0.00 2.00 4.00 6.00 m

12.00

10.00

8.00

6.00

4.00

2.00

0.00

-2.00

0.301

0 .3 00

0 .299

0.298

0.296

0.2 940. 29 2 0.2900.2 86

0.283

0.282

0.278

0.278

0.275

0.2 72

0.272

0.268

0. 268

0.2 65

0.2 65

0. 26 4

Vector of nodal displacements, Loadcase 105 MAX-VY, 1 cmspacious = 4.00 mm (Max=0.301)

M 1 : 100

XYZ

-1177 -1058-7

90.3 758.8758.8

661.8

606.6

606.6

540.5

470.2

435.3

393.4

-364.7

220.3

114.7

-114.6 -96.6

55.0

-54.8 52.2

47.9

37.5

25.5

25.4

-21.1

16.0

-13.9-13.3

Sector of system Beams Group 1 2Beam bending moment My, nonlinear Loadcase 21 PHASE IV: Swell..Loading 10.0%, 1 cm spacious = 1500. kNm (Min=-1177.)(Max=758.8)

-4.00 -2.00 0.00 2.00 4.00 6.00 m

12.00

10.00

8.00

6.00

4.00

2.00

0.00

-2.00

M 1 : 100

XYZ


-4.00 -2.00 0.00 2.00 4.00 6.00 m

12.00

10.00

8.00

6.00

4.00

2.00

0.00

-2.00

1 .01

0 .865 0 .8 63

0.777

0.73

2

0 .7 25

0.6460.614

0.600

0.600

0.598

0.587

0.578

0.554

0.549

0.5220.4

76

0.465

0.4400.435

0.2800.277


M 1 : 100

XYZ

-2019 -1821

-136

9

12681268

1129

1009

1009

890.4

807.2

705.8

682.9

-635.6

391.0

-202.9

171.5

-99.3-99.091.6

86.5

66.4

54.4

49.4

43.7

-37.1

29.1

-19.3-18.4

Sector of system Beams Group 1 2Beam bending moment My, nonlinear Loadcase 23 PHASE IV: Swell..Loading 20.0%, 1 cm spacious = 1500. kNm (Min=-2019.)(Max=1268.)

-4.00 -2.00 0.00 2.00 4.00 6.00 m

12.00

10.00

8.00

6.00

4.00

2.00

0.00

-2.00

M 1 : 100

XYZ


-4.00 -2.00 0.00 2.00 4.00 6.00 m

12.00

10.00

8.00

6.00

4.00

2.00

0.00

-2.00

1 .58

1 .55

1 .4 7

1.46

1 .33

1.3 2

1.25 1.22

1.111.05

0.975

0.927

0.919

0.86

5

0.863

0.8590.74

1

0.737 0.724

0.705

0.601 0.577


M 1 : 100

XYZ

-2701 -2440

-184

7

16661666

1499

1321

1321

1164

1077

914.1

913.4

-860.9

530.8

-277.2

212.1

-137.9-137.5

122.2115.1

91.8

81.5

59.8

-49.4

42.2

40.6

-21.8-19.8


-4.00 -2.00 0.00 2.00 4.00 6.00 m

12.0

010

.00

8.00

6.00

4.00

2.00

0.00

-2.0

0

M 1 : 100

XYZ


-4.00 -2.00 0.00 2.00 4.00 6.00 m

12.0

010

.00

8.00

6.00

4.00

2.00

0.00

-2.0

0

2 .1 9

2 .0 8

2. 07

2 .0 7

1.78 1.75

1 .7 3

1.72

1.501.44

1.32

1.26

1.24

1.17

1.09

1.08

0.998

0.981

0.979

0.927

0.899 0.866


M 1 : 100

XYZ

-380

4

-2631 -2530

22912291

2084

1819

1819

1595

513

1281

1244

-1240

749.5557.2

-401.7

268.2

-204.8174.5

164.0

135.9

89.2

-65.8

59.5-54.0

22.1

-21.7-16.1


-4.00 -2.00 0.00 2.00 4.00 6.00 m

12.0

010

.00

8.00

6.00

4.00

2.00

0.00

-2.0

0

M 1 : 100

XYZ


-4.00 -2.00 0.00 2.00 4.00 6.00 m

12.0

010

.00

8.00

6.00

4.00

2.00

0.00

-2.0

0

3 .23

3 .0 8

3.05

2 .89

2.65 2.60

2 .39

2.38

2.162.09

1.89

1.82

1.78

1.71

1.47

1.46

1.44 1.41

1.40

1.39 1.34

1.32


M 1 : 100

XYZ

-467

5

-325

4 -3124

27732773

2539

2205

205

1927

55

1562

-1546

1498

912.1683.3

-506.4

304.5

-261.4220.0

207.1

174.2

117.8

75.4

-75.2

-72.1

-17.1-8.49

-1.37


-4.00 -2.00 0.00 2.00 4.00 6.00 m

12.0

010

.00

8.00

6.00

4.00

2.00

0.00

-2.0

0

M 1 : 100

XYZ


-4.00 -2.00 0.00 2.00 4.00 6.00 m

12.0

010

.00

8.00

6.00

4.00

2.00

0.00

-2.0

0

4 .05

3 .8 7

3.84

3 .58

3.34 3.28

2 .95

2.94

2.692.61

2.34

2.29

2.21

2.16

1.79

1.781.78

1.781.76

1.75

1.72

1.66


M 1 : 100

XYZ

-5723

-4008 -3854

33553355

3094

2671

71

2317

3 -1937

1894

1800

1102822.8

-640.9 -334.6

327.5

280.7266.4

223.5

159.7

-97.1

93.5

-79.5

-38.6

5.64-4.00


-4.00 -2.00 0.00 2.00 4.00 6.00 m

12.0

010

.00

8.00

6.00

4.00

2.00

0.00

-2.0

0

M 1 : 100

XYZ


-4.00 -2.00 0.00 2.00 4.00 6.00 m

12.0

010

.00

8.00

6.00

4.00

2.00

0.00

-2.0

0

5 .05

4 .8 3

4.79

4 .46

4.1 7 4.11

3 .68

3.65

3.343.27

2.89

2.88

2.75

2.74

2.24

2.23

2.202.20

2.20

2.18

2.101.80




FEM simulation of high-speed railway track in swellable soil

Soil Exchange

Excavation step 1

Sand

Swellable Clay

Rock

Railway Dam

Excavation step 2



Displacement FEM framework with incremental (time stepping) global solution strategy

σ∆ ⇒ ∆ε



Displacement FEM framework with incremental(time stepping) global solution strategy

σ∆ ⇒ ∆ε

Additive strain decomposition

e q plt t t q pl

⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠

+∆

∆ =∆ +∆ +∆

= − +∆ +∆

ε ε ε ε

C σ σ ε ε


Numerical studies

The proposed model was implemented into thegeotechnical finite element program TALPA thatwas used for subsequent numerical simulations



2nd excavation step , ∆t = 0.5 a

A Viscous Continuum Mechanics Approach - NAFEMS · A Viscous Continuum Mechanics Approach H....

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Transcript of A Viscous Continuum Mechanics Approach - NAFEMS · A Viscous Continuum Mechanics Approach H....